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On Augmented Lagrangian Methods with General Lower-Level Constraints

https://doi.org/10.1137/060654797
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Outgoing claims: the papers this work cites, builds on, or argues with.

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Practical Methods of Optimization
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Inexact Restoration Methods for Nonlinear Programming: Advances and Perspectives
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Lie Group Methods for Optimization with Orthogonality Constraints
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More Test Examples for Nonlinear Programming Codes
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Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A)
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Multiplier and gradient methods
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A globally convergent method for nonlinear programming
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The multiplier method of Hestenes and Powell applied to convex programming
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A semidefinite framework for trust region subproblems with applications to large scale minimization
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A trust region method based on interior point techniques for nonlinear programming
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An augmented Lagrangian interior-point method using directions of negative curvature
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On the convergence of Newton iterations to non-stationary points
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A globally convergent primal-dual interior-point filter method for nonlinear programming
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An algorithm for nonlinear optimization using linear programming and equality constrained subproblems
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A primal-dual trust region algorithm for nonlinear optimization
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On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
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An interior algorithm for nonlinear optimization that combines line search and trust region steps
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Interior-point ℓ2-penalty methods for nonlinear programming with strong global convergence properties
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Augmented Lagrangian methods under the constant positive linear dependence constraint qualification
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A primal-dual trust-region algorithm for non-convex nonlinear programming
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Interior-point methods for nonconvex nonlinear programming: orderings and higher-order methods
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Benchmarking optimization software with performance profiles
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Numerical Comparison of Augmented Lagrangian Algorithms for Nonconvex Problems
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Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization
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On the Relation between Constant Positive Linear Dependence Condition and Quasinormality Constraint Qualification
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Augmented Lagrangian Algorithms Based on the Spectral Projected Gradient Method for Solving Nonlinear Programming Problems
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The Fritz John necessary optimality conditions in the presence of equality and inequality constraints
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Constrained Optimization and Lagrange Multiplier Methods
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On Khachiyan's algorithm for the computation of minimum-volume enclosing ellipsoids
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Duality-based domain decomposition with natural coarse-space for variational inequalities
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Numerical optimization
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Mathematical Programs with Equilibrium Constraints
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Validation of an Augmented Lagrangian Algorithm with a Gauss-Newton Hessian Approximation Using a Set of Hard-Spheres Problems
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On the Global Convergence of a Modified Augmented Lagrangian Linesearch Interior-Point Newton Method for Nonlinear Programming
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Inexact-Restoration Method with Lagrangian Tangent Decrease and New Merit Function for Nonlinear Programming
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Large-Scale Active-Set Box-Constrained Optimization Method with Spectral Projected Gradients
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A Simple Primal-Dual Feasible Interior-Point Method for Nonlinear Programming with Monotone Descent
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Feasible Interior Methods Using Slacks for Nonlinear Optimization
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The trust-region self-consistent field method: Towards a black-box optimization in Hartree–Fock and Kohn–Sham theories
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Globally convergent trust-region methods for self-consistent field electronic structure calculations
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Discrete Newton's method with local variations for solving large-scale nonlinear systems
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Inexact spectral projected gradient methods on convex sets
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Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming
inferredcites →https://doi.org/10.1137/0728030openalex-snapshot
A Globally Convergent Augmented Lagrangian Algorithm for Optimization with General Constraints and Simple Bounds
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Computing Optimal Locally Constrained Steps
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Computing a Trust Region Step
inferredcites →https://doi.org/10.1137/1.9780898719857openalex-snapshot
Trust Region Methods
inferredcites →https://doi.org/10.1137/1035044openalex-snapshot
Lagrange Multipliers and Optimality
inferredcites →https://doi.org/10.1137/s0036142903436393openalex-snapshot
Inexact Semimonotonic Augmented Lagrangians with Optimal Feasibility Convergence for Convex Bound and Equality Constrained Quadratic Programming
inferredcites →https://doi.org/10.1137/s0036144502414942openalex-snapshot
Interior Methods for Nonlinear Optimization
inferredcites →https://doi.org/10.1137/s0036144504446096openalex-snapshot
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
inferredcites →https://doi.org/10.1137/s0895479895290954openalex-snapshot
The Geometry of Algorithms with Orthogonality Constraints
inferredcites →https://doi.org/10.1137/s1052623400370515openalex-snapshot
Superlinear Convergence of Primal-Dual Interior Point Algorithms for Nonlinear Programming
inferredcites →https://doi.org/10.1137/s1052623401392123openalex-snapshot
A Primal-Dual Interior-Point Method for Nonlinear Programming with Strong Global and Local Convergence Properties
inferredcites →https://doi.org/10.1137/s1052623401399320openalex-snapshot
A Globally Convergent Filter Method for Nonlinear Programming
inferredcites →https://doi.org/10.1137/s1052623402400641openalex-snapshot
A Robust Primal-Dual Interior-Point Algorithm for Nonlinear Programs
inferredcites →https://doi.org/10.1137/s1052623493251463openalex-snapshot
Convergence Properties of an Augmented Lagrangian Algorithm for Optimization with a Combination of General Equality and Linear Constraints
inferredcites →https://doi.org/10.1137/s1052623494266365openalex-snapshot
The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization Problem
inferredcites →https://doi.org/10.1137/s1052623497326629openalex-snapshot
On the Constant Positive Linear Dependence Condition and Its Application to SQP Methods
inferredcites →https://doi.org/10.1137/s1052623497330963openalex-snapshot
Nonmonotone Spectral Projected Gradient Methods on Convex Sets
inferredcites →https://doi.org/10.1137/s105262349928887xopenalex-snapshot
A New Matrix-Free Algorithm for the Large-Scale Trust-Region Subproblem
inferredcites →https://doi.org/10.1137/s1052623499355533openalex-snapshot
An Interior Point Method with a Primal-Dual Quadratic Barrier Penalty Function for Nonlinear Optimization
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Global Convergence of a Trust-Region SQP-Filter Algorithm for General Nonlinear Programming
inferredcites →https://doi.org/10.1137/s1052623499357945openalex-snapshot
Convergent Infeasible Interior-Point Trust-Region Methods for Constrained Minimization
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Augmented Lagrangians with Adaptive Precision Control for Quadratic Programming with Simple Bounds and Equality Constraints
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CUTE
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Algorithm 813
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GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization
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Practical Methods of Optimization.
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Sphere Packings, Lattices and Groups.
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Iterative methods for linear and nonlinear equations

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Existence of augmented Lagrange multipliers: reduction to exact penalty functions and localization principle
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Improved local convergence results for augmented Lagrangian methods in $${\varvec{C}}^\mathbf{2}$$C2-cone reducible constrained optimization
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Optimality conditions and global convergence for nonlinear semidefinite programming
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An augmented Lagrangian method for optimization problems with structured geometric constraints
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A semismooth Newton based augmented Lagrangian method for nonsmooth optimization on matrix manifolds
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Constrained composite optimization and augmented Lagrangian methods
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First- and second-order optimality conditions for second-order cone and semidefinite programming under a constant rank condition
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A minimal face constant rank constraint qualification for reducible conic programming
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Computing equilibria in economies with incomplete markets, collateral and default penalties
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Novel green strategy to improve the hydrophobicity of cellulose nanocrystals and the interfacial elasticity of Pickering emulsions
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Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization
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Second-order negative-curvature methods for box-constrained and general constrained optimization
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Proximal methods for nonlinear programming: double regularization and inexact subproblems
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Local convergence of the method of multipliers for variational and optimization problems under the noncriticality assumption
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Markov–Dubins path via optimal control theory
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Augmented Lagrangian methods for nonlinear programming with possible infeasibility
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Nonconvex and Nonsmooth Optimization with Generalized Orthogonality Constraints: An Approximate Augmented Lagrangian Method
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Moreau Envelope Augmented Lagrangian Method for Nonconvex Optimization with Linear Constraints
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Sorted $$L_1/L_2$$ Minimization for Sparse Signal Recovery
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Convergence Properties of Modified and Partially-Augmented Lagrangian Methods for Mathematical Programs with Complementarity Constraints
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Constant-Rank Condition and Second-Order Constraint Qualification
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On Approximate KKT Condition and its Extension to Continuous Variational Inequalities
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Outer Trust-Region Method for Constrained Optimization
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A Gauss–Newton Approach for Solving Constrained Optimization Problems Using Differentiable Exact Penalties
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A New Scalarization Technique to Approximate Pareto Fronts of Problems with Disconnected Feasible Sets
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Some Results on Augmented Lagrangians in Constrained Global Optimization via Image Space Analysis
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Global Optimization of Protein–peptide Docking by a Filling Function Method
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Newton-Type Methods: A Broader View
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Convergence Results of an Augmented Lagrangian Method Using the Exponential Penalty Function
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The Use of Squared Slack Variables in Nonlinear Second-Order Cone Programming
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An Augmented Lagrangian Method for Equality Constrained Optimization with Rapid Infeasibility Detection Capabilities
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An Augmented Lagrangian Method for Cardinality-Constrained Optimization Problems
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An Augmented Lagrangian Method Exploiting an Active-Set Strategy and Second-Order Information
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Infeasible and Critically Feasible Optimal Control
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Bounds of the Solution Set to the Polynomial Complementarity Problem
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A Practical Second-Order Optimality Condition for Cardinality-Constrained Problems with Application to an Augmented Lagrangian Method
inferred← citeshttps://doi.org/10.1007/s10957-025-02731-3openalex-snapshot
Global Convergence of a Second-order Augmented Lagrangian Method Under an Error Bound Condition
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On the Global Convergence of a General Class of Augmented Lagrangian Methods
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Enhancing Sharp Augmented Lagrangian Methods with Smoothing Techniques for Nonlinear Programming
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Partial spectral projected gradient method with active-set strategy for linearly constrained optimization
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Handling infeasibility in a large-scale nonlinear optimization algorithm
inferred← citeshttps://doi.org/10.1007/s11075-020-00928-3openalex-snapshot
On constrained optimization with nonconvex regularization
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On the best achievable quality of limit points of augmented Lagrangian schemes
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A PDE-informed optimization algorithm for river flow predictions
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A matrix-free augmented lagrangian algorithm with application to large-scale structural design optimization
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The Josephy–Newton Method for Semismooth Generalized Equations and Semismooth SQP for Optimization
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New Constraint Qualifications and Optimality Conditions for Second Order Cone Programs
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On the minimization of possibly discontinuous functions by means of pointwise approximations
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A note on approximate Karush–Kuhn–Tucker conditions in locally Lipschitz multiobjective optimization
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Convergence of a special partially augmented Lagrangian algorithm for sparsity-constrained optimization problems
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Generalized order-value optimization
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Comments on: Critical Lagrange multipliers: what we currently know about them, how they spoil our lives, and what we can do about it
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Critical Lagrange multipliers: what we currently know about them, how they spoil our lives, and what we can do about it
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On the solution of linearly constrained optimization problems by means of barrier algorithms
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Improving performance of open-pit mine production scheduling problem under grade uncertainty by hybrid algorithms
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An effective MIP model based on grey wolf optimizer for lot-sizing LTPSOP in open-pit mines under uncertainty
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Optimization of the production scheduling problem in open-pit mines to maximize the net present value using the human mental search algorithm
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TACO: a toolkit for AMPL control optimization
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On scaled stopping criteria for a safeguarded augmented Lagrangian method with theoretical guarantees
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PDLP: a practical first-order method for large-scale linear programming
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A second-order convergence augmented Lagrangian method using non-quadratic penalty functions
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Solving LTPSOP in open-pit mines using Gaussian process and human mental search
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On the application of an augmented Lagrangian algorithm to some portfolio problems
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An Augmented Lagrangian algorithm for nonlinear semidefinite programming applied to the covering problem
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A support tool for planning classrooms considering social distancing between students
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On Approximate Karush–Kuhn–Tucker Conditions for Multiobjective Optimization Problems
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Production scheduling problem and solver improvement via integration of the grey wolf optimizer into the augmented Lagrangian relaxation method
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Practical Augmented Lagrangian Methods
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Energy-efficient QoS-based OCDMA networks aided by nonlinear programming methods
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The global convergence of augmented Lagrangian methods based on NCP function in constrained nonconvex optimization
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A subspace version of the Wang–Yuan Augmented Lagrangian-Trust Region method for equality constrained optimization
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An augmented Lagrangian approach for cardinality constrained minimization applied to variable selection problems
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Dynamics of Nuclear Receptor Helix-12 Switch of Transcription Activation by Modeling Time-Resolved Fluorescence Anisotropy Decays
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Modified subspace limited memory BFGS algorithm for large-scale bound constrained optimization
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An augmented Lagrangian fish swarm based method for global optimization
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Assessing the reliability of general-purpose Inexact Restoration methods
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Convergence analysis of modified p th power Lagrangian algorithms with alternative updating strategies for constrained nonconvex optimization
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Efficient method for symmetric nonnegative matrix factorization with an approximate augmented Lagrangian scheme
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Orthogonal packing of identical rectangles within isotropic convex regions
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Trajectory optimization learning for fixed-wing aircraft
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Production planning and scheduling integration through augmented Lagrangian optimization
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Minimizing the object dimensions in circle and sphere packing problems
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New and improved results for packing identical unitary radius circles within triangles, rectangles and strips
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An exact method to find a circle passing through two points and minimizing the maximal weighted distance to a set of points
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Mathematical optimization of procedures for cryoprotectant equilibration using a toxicity cost function
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MolShaCS: A free and open source tool for ligand similarity identification based on Gaussian descriptors
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Global convergence of a robust filter SQP algorithm
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Deterministic and stochastic global optimization techniques for planar covering with ellipses problems
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A matheuristic approach with nonlinear subproblems for large-scale packing of ellipsoids
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Using a modified genetic algorithm to minimize the production costs for slabs of precast prestressed concrete joists
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A local saddle point for the hyperbolic augmented Lagrangian function
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A physically based Proper Orthogonal Decomposition for structural mechanics involving dissipative processes
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Two-Phase Approach to the Nesting problem with continuous rotations
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Regularized Interior Point Methods for Constrained Optimization and Control
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Augmented Lagrangian Guided Learning for the Optimal Power Flow Problem
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Sparse recovery under nonnegativity and sum-to-one constraints
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A parallel-in-time multiple shooting algorithm for large-scale PDE-constrained optimal control problems
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Distributed pose graph optimization based on alternating direction method of multipliers: The EPALMAL algorithm
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Multi-scale active patches fusion based on spatiotemporal LBP-TOP for micro-expression recognition
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On optimization strategies for parameter estimation in models governed by partial differential equations
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A dynamical neural network approach for solving stochastic two-player zero-sum games
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Convergence detection for optimization algorithms: Approximate-KKT stopping criterion when Lagrange multipliers are not available
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An infeasibility certificate for nonlinear programming based on Pareto criticality condition
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An example comparing the standard and safeguarded augmented Lagrangian methods
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On the convergence of inexact augmented Lagrangian methods for problems with convex constraints
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A new Lagrangian-based first-order method for nonconvex constrained optimization
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A feasible method for constrained derivative-free optimization
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Augmented Lagrangian combined to evolutionary heuristic for energy efficiency in OCDMA networks
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A constraint qualification for the dislocation hyperbolic augmented Lagrangian algorithm
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Efficient focused energy delivery with grating lobe mitigation for precision electronic warfare
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Channel-denoising-enhanced DRL for robust beamforming in outage-constrained dual-function radar–communication systems
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SdeaR: Stochastic data envelopment analysis with R
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An inner–outer nonlinear programming approach for constrained quadratic matrix model updating
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Wrapping Up Viruses at Multiscale Resolution: Optimizing PACKMOL and SIRAH Execution for Simulating the Zika Virus
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Hopfield learning‐based and non‐linear programming methods for resource allocation in OCDMA networks
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Equality‐embedded augmented Lagrangian neural network for DC optimal power flow
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Constraints‐Embedding Neural Network for Economic Dispatch Considering Dynamic Total Transfer Capability
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Curves of minimax spirality
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Dislocation hyperbolic augmented Lagrangian algorithm for nonconvex optimization
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On second-order optimality conditions for nonlinear programming
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On sequential optimality conditions for smooth constrained optimization
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An exact penalty-Lagrangian approach for large-scale nonlinear programming
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Global convergence of a derivative-free inexact restoration filter algorithm for nonlinear programming
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A generalized proximal-point method for convex optimization problems in Hilbert spaces
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Augmented Lagrangians quadratic growth and second-order sufficient optimality conditions
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A primal–dual penalty method via rounded weighted-ℓ1 Lagrangian duality
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