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LMI Approximations for Cones of Positive Semidefinite Forms

https://doi.org/10.1137/03060151x
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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The Moment Problem on Compact Semi-Algebraic Sets
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Real Algebraic Geometry
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Positive Polynomials: From Hilbert’s 17th Problem to Real Algebra
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Class of global minimum bounds of polynomial functions
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Ueber die Darstellung definiter Formen als Summe von Formenquadraten
inferredcites →https://doi.org/10.1007/bf01446568openalex-snapshot
TheK-moment problem for compact semi-algebraic sets
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Uniform denominators in Hilbert's seventeenth problem
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Some NP-complete problems in quadratic and nonlinear programming
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Modifiedr-algorithm to find the global minimum of polynomial functions
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Positive polynomials on compact sets
inferredcites →https://doi.org/10.1007/s10107-003-0387-5openalex-snapshot
Semidefinite programming relaxations for semialgebraic problems
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Semidefinite representations for finite varieties
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Global optimization of rational functions: a semidefinite programming approach
inferredcites →https://doi.org/10.1016/s0022-4049(00)00155-9openalex-snapshot
A new bound for Pólya's Theorem with applications to polynomials positive on polyhedra
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On non-negative forms in real variables some or all of which are non-negative
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Solving Standard Quadratic Optimization Problems via Linear, Semidefinite and Copositive Programming
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Global Minimization of a Multivariate Polynomial using Matrix Methods
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Some concrete aspects of Hilbert’s 17th Problem
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Mathematical problems
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A Mathematical View of Interior-Point Methods in Convex Optimization
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Numerical Linear Algebra
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Global Optimization with Polynomials and the Problem of Moments
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Approximation of the Stability Number of a Graph via Copositive Programming
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Optimal Inequalities in Probability Theory: A Convex Optimization Approach
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Bounds on measures satisfying moment conditions
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A Conic Programming Approach to Generalized Tchebycheff Inequalities
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A Semidefinite Programming Approach to Optimal-Moment Bounds for Convex Classes of Distributions
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A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0–1 Programming
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Convex Analysis
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A GENERAL FRAMEWORK FOR CONVEX RELAXATION OF POLYNOMIAL OPTIMIZATION PROBLEMS OVER CONES
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Representing polynomials by positive linear functions on compact convex polyhedra
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Matrix Computations
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Real algebraic geometry
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Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization

What points at this work

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

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A Linear Programming Reformulation of the Standard Quadratic Optimization Problem
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On an extension of Pólya’s Positivstellensatz
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Completely positive and completely positive semidefinite tensor relaxations for polynomial optimization
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Approximation hierarchies for copositive cone over symmetric cone and their comparison
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Alternative SDP and SOCP approximations for polynomial optimization
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Computing the Stability Number of a Graph Via Linear and Semidefinite Programming
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KKT Solution and Conic Relaxation for Solving Quadratically Constrained Quadratic Programming Problems
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Computational Complexity of Sum-of-Squares Bounds for Copositive Programs
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A Conic Programming Approach to Generalized Tchebycheff Inequalities
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Finding Minimum Volume Circumscribing Ellipsoids Using Generalized Copositive Programming
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