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Optimality criteria and duality in multiple-objective optimization involving generalized invexity

https://doi.org/10.1007/bf02207775

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inferred← citeshttps://doi.org/10.1006/jmaa.1996.0080openalex-snapshot

ϵ-Pareto Optimality for Nondifferentiable Multiobjective Programming via Penalty Function

inferred← citeshttps://doi.org/10.1006/jmaa.1997.5238openalex-snapshot

Optimality and Duality in Nondifferentiable Multiobjective Optimization Involvingd-Type I and Related Functions

inferred← citeshttps://doi.org/10.1006/jmaa.1997.5786openalex-snapshot

On Minimax Fractional Optimality Conditions with Invexity

inferred← citeshttps://doi.org/10.1006/jmaa.1998.5992openalex-snapshot

On Multiple-Objective Optimization with Generalized Univexity

inferred← citeshttps://doi.org/10.1006/jmaa.1998.6256openalex-snapshot

Optimality Conditions and Duality for Multiobjective Variational Problems with Generalized B-Invexity

inferred← citeshttps://doi.org/10.1006/jmaa.1999.6284openalex-snapshot

Generalized Convexity in Multiobjective Programming

inferred← citeshttps://doi.org/10.1006/jmaa.2001.7542openalex-snapshot

Multiobjective Programming under Generalized Type I Invexity

inferred← citeshttps://doi.org/10.1007/0-306-48107-3_2openalex-snapshot

Nonlinear Multiobjective Programming

inferred← citeshttps://doi.org/10.1007/0-387-23639-2_19openalex-snapshot

New Generalized Invexity for Duality in Multiobjective Programming Problems Involving N-Set Functions

inferred← citeshttps://doi.org/10.1007/0-387-23639-2_7openalex-snapshot

Duality in Multiobjective Optimization Problems with Set Constraints

inferred← citeshttps://doi.org/10.1007/978-0-387-74759-0_419openalex-snapshot

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inferred← citeshttps://doi.org/10.1007/bf03399226openalex-snapshot

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inferred← citeshttps://doi.org/10.1007/s00186-007-0202-9openalex-snapshot

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inferred← citeshttps://doi.org/10.1007/s10255-005-0284-1openalex-snapshot

Duality Theorems on Multi-objective Programming of Generalized Functions

inferred← citeshttps://doi.org/10.1007/s10898-005-1653-2openalex-snapshot

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inferred← citeshttps://doi.org/10.1007/s10898-007-9150-4openalex-snapshot

Sufficiency in multiobjective subset programming involving generalized type-I functions

inferred← citeshttps://doi.org/10.1007/s10898-007-9196-3openalex-snapshot

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inferred← citeshttps://doi.org/10.1007/s10898-008-9298-6openalex-snapshot

On G-invex multiobjective programming. Part II. Duality

inferred← citeshttps://doi.org/10.1007/s10898-008-9299-5openalex-snapshot

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inferred← citeshttps://doi.org/10.1007/s10898-009-9418-yopenalex-snapshot

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inferred← citeshttps://doi.org/10.1007/s10898-024-01367-3openalex-snapshot

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inferred← citeshttps://doi.org/10.1007/s10957-007-9271-4openalex-snapshot

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inferred← citeshttps://doi.org/10.1007/s11424-011-8234-xopenalex-snapshot

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inferred← citeshttps://doi.org/10.1007/s11590-009-0159-0openalex-snapshot

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inferred← citeshttps://doi.org/10.1007/s12190-008-0069-9openalex-snapshot

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inferred← citeshttps://doi.org/10.1007/s12215-026-01401-1openalex-snapshot

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inferred← citeshttps://doi.org/10.1007/s12351-015-0206-9openalex-snapshot

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inferred← citeshttps://doi.org/10.1007/s12597-015-0214-9openalex-snapshot

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inferred← citeshttps://doi.org/10.1007/s12597-015-0242-5openalex-snapshot

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inferred← citeshttps://doi.org/10.1007/s12597-023-00674-9openalex-snapshot

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inferred← citeshttps://doi.org/10.1007/s40305-019-00269-6openalex-snapshot

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inferred← citeshttps://doi.org/10.1007/s40819-021-01002-9openalex-snapshot

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inferred← citeshttps://doi.org/10.1007/s40995-017-0156-6openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/0898-1221(96)00106-xopenalex-snapshot

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inferred← citeshttps://doi.org/10.1016/j.amc.2014.04.066openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/j.cam.2006.06.009openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/j.cam.2008.07.028openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/j.camwa.2006.02.004openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/j.camwa.2006.08.006openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/j.camwa.2007.05.002openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/j.ejor.2005.02.062openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/j.ejor.2009.04.018openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/j.ins.2005.08.003openalex-snapshot

Second order (F,α,ρ,d)-convexity and duality in multiobjective programming

inferred← citeshttps://doi.org/10.1016/j.jmaa.2003.12.042openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/j.jmaa.2004.08.036openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/j.jmaa.2005.02.018openalex-snapshot

Generalized type I invexity and duality in multiobjective variational problems

inferred← citeshttps://doi.org/10.1016/j.jmaa.2005.02.032openalex-snapshot

Multiple objective fractional programming involving semilocally type I-preinvex and related functions

inferred← citeshttps://doi.org/10.1016/j.jmaa.2005.02.064openalex-snapshot

Sufficiency and duality in nondifferentiable multiobjective programming involving generalized type I functions

inferred← citeshttps://doi.org/10.1016/j.jmaa.2005.04.067openalex-snapshot

Some nondifferentiable multiobjective programming problems

inferred← citeshttps://doi.org/10.1016/j.jmaa.2006.05.026openalex-snapshot

Nonsmooth multiobjective optimization using limiting subdifferentials

inferred← citeshttps://doi.org/10.1016/j.mcm.2008.05.054openalex-snapshot

A characterization of pseudoinvexity in multiobjective programming

inferred← citeshttps://doi.org/10.1016/j.mcm.2011.01.034openalex-snapshot

A new characterization of (weak) Pareto optimality for differentiable vector optimization problems with G -invex functions

inferred← citeshttps://doi.org/10.1016/j.na.2005.05.008openalex-snapshot

An -approximation method in nonlinear vector optimization

inferred← citeshttps://doi.org/10.1016/j.na.2007.02.033openalex-snapshot

Optimality for nonsmooth fractional multiple objective programming

inferred← citeshttps://doi.org/10.1016/j.na.2007.11.039openalex-snapshot

Generalized -univexity and duality for nondifferentiable minimax fractional programming

inferred← citeshttps://doi.org/10.1016/j.na.2009.03.013openalex-snapshot

Nonsmooth multiple-objective optimization in separable Hilbert spaces

inferred← citeshttps://doi.org/10.1016/j.na.2010.06.019openalex-snapshot

Generalized convexity and efficiency for non-regular multiobjective programming problems with inequality-type constraints

inferred← citeshttps://doi.org/10.1016/j.na.2011.05.058openalex-snapshot

On sufficiency and duality for nonsmooth multiobjective programming problems involving generalized -invex functions

inferred← citeshttps://doi.org/10.1016/j.rico.2024.100395openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/s0377-0427(03)00455-2openalex-snapshot

Nondifferentiable minimax fractional programming under generalized univexity

inferred← citeshttps://doi.org/10.1016/s0377-2217(03)00439-9openalex-snapshot

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inferred← citeshttps://doi.org/10.1016/s0898-1221(03)00133-0openalex-snapshot

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inferred← citeshttps://doi.org/10.1023/a:1008321026317openalex-snapshot

Generalized Invexity and Duality in Multiobjective Programming Problems

inferred← citeshttps://doi.org/10.1023/a:1026041403408openalex-snapshot

Efficiency Conditions and Duality for a Class of Multiobjective Fractional Programming Problems

inferred← citeshttps://doi.org/10.1023/b:jogo.0000047911.03061.88openalex-snapshot

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inferred← citeshttps://doi.org/10.1023/b:jogo.0000047912.69270.8copenalex-snapshot

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inferred← citeshttps://doi.org/10.1051/itmconf/20192401002openalex-snapshot

E-invexity and generalized E-invexity in E-differentiable multiobjective programming

inferred← citeshttps://doi.org/10.1051/ro/2014046openalex-snapshot

Fritz John type optimality and duality in nonlinear programming under weak pseudo-invexity

inferred← citeshttps://doi.org/10.1080/00207160701864442openalex-snapshot

On optimality and duality for multiple-objective optimization under generalized type I univexity

inferred← citeshttps://doi.org/10.1080/01630560701749664openalex-snapshot

Second-Order Duality in Multiobjective Programming Involving ( F , α, ρ, d )-V-Type I Functions

inferred← citeshttps://doi.org/10.1080/01630560802418409openalex-snapshot

Duality in Vector Optimization Under Type 1 α-Invexity in Banach Spaces

inferred← citeshttps://doi.org/10.1080/01630560902841187openalex-snapshot

Multiobjective Problems with Nonsmooth Equality Constraints

inferred← citeshttps://doi.org/10.1080/02331939608844188openalex-snapshot

Optimality and duality for multiobjective fractional programming involving nonsmooth($si:F$esi:ρ)–convex functions

inferred← citeshttps://doi.org/10.1080/02331939608844194openalex-snapshot

Optimality and duality for multiobjective fractional programming involving nonsmooth pseudoinvex functions

inferred← citeshttps://doi.org/10.1080/02331939708844277openalex-snapshot

Sufficiency criteria and duality in complex nonlinear programming involving pseudoinvex function

inferred← citeshttps://doi.org/10.1080/02331939708844289openalex-snapshot

A survey of recent[1985-1995]advances in generalized convexity with applications to duality theory and optimality conditions

inferred← citeshttps://doi.org/10.1080/02331939808844418openalex-snapshot

Sufficient optimality criteria and duality for nondifferentiable fractional variational problems with generalized (F, ρ)-convexity

inferred← citeshttps://doi.org/10.1080/09720502.2007.10700525openalex-snapshot

On nonsmooth multiobjective programming with generalized univexity

inferred← citeshttps://doi.org/10.1080/09720510.2021.1890907openalex-snapshot

E-duality results for E-differentiable vector optimization problems involving E-type I functions

inferred← citeshttps://doi.org/10.1081/nfa-100108308openalex-snapshot

SUFFICIENT OPTIMALITY CONDITIONS AND DUALITY IN MULTIOBJECTIVE OPTIMIZATION INVOLVING GENERALIZED CONVEXITY

inferred← citeshttps://doi.org/10.1081/nfa-200045804openalex-snapshot

Second Order Duality in Multiobjective Programming Involving Generalized Type I Functions

inferred← citeshttps://doi.org/10.1088/1742-6596/1294/3/032027openalex-snapshot

E-Duality Results For E-Differentiable E-Invex Multiobjective Programming Problems

inferred← citeshttps://doi.org/10.1109/cso.2010.230openalex-snapshot

Duality for Multiobjective Optimization Involving Extended (F, alpha, rho, d)-type I Functions

inferred← citeshttps://doi.org/10.1109/cso.2011.247openalex-snapshot

Sufficiency in Multiobjective Programming Involving Extended (F, alpha, rho, d)-type I Functions

inferred← citeshttps://doi.org/10.1109/fskd.2007.154openalex-snapshot

An Equivalent Vector Optimization Problem for Nonsmooth Multiobjective Programming Problem

inferred← citeshttps://doi.org/10.11121/ijocta.01.2014.00178openalex-snapshot

A class of semilocal E-preinvex maps in Banach spaces with applications to nondiﬀerentiable vector optimization

inferred← citeshttps://doi.org/10.11121/ijocta.01.2016.00282openalex-snapshot

On semi-G-V-type I concepts for directionally differentiable multiobjective programming problems

inferred← citeshttps://doi.org/10.1137/070710664openalex-snapshot

Nonsmooth Optimization Using Mordukhovich's Subdifferential

inferred← citeshttps://doi.org/10.1142/s0217595906001029openalex-snapshot

AN η-APPROXIMATION APPROACH IN NONLINEAR VECTOR OPTIMIZATION WITH UNIVEX FUNCTIONS

inferred← citeshttps://doi.org/10.1142/s0219622014500394openalex-snapshot

Generalized Convexity and Characterization of (Weak) Pareto-Optimality in Nonsmooth Multiobjective Optimization Problems

inferred← citeshttps://doi.org/10.1142/s1793557119500888openalex-snapshot

Efficiency and duality for vector optimization problem on Riemannian manifolds involving KT-B-invexity

inferred← citeshttps://doi.org/10.1155/2010/172059openalex-snapshot

Optimality Conditions in Nondifferentiable G-Invex Multiobjective Programming

inferred← citeshttps://doi.org/10.1155/2010/898626openalex-snapshot

Optimality and Duality in Nonsmooth Multiobjective Optimization Involving V-Type I Invex Functions

inferred← citeshttps://doi.org/10.1155/2013/383692openalex-snapshot

Univex Interval-Valued Mapping with Differentiability and Its Application in Nonlinear Programming

inferred← citeshttps://doi.org/10.1155/2014/524698openalex-snapshot

GeodesicB-Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds

inferred← citeshttps://doi.org/10.11948/2015001openalex-snapshot

SECOND ORDER NONDIFFERENTIABLE MULTIOBJECTIVE FRACTIONAL PROGRAMMING UNDER GENERALIZED UNIVEX FUNCTIONS

inferred← citeshttps://doi.org/10.11948/20180261openalex-snapshot

HIGHER ORDER DUALITY FOR A NEW CLASS OF NONCONVEX SEMI-INFINITE MULTIOBJECTIVE FRACTIONAL PROGRAMMING WITH SUPPORT FUNCTIONS

inferred← citeshttps://doi.org/10.12732/ijpam.v87i4.1openalex-snapshot

ON A NONDIFFERENTIABLE VECTOR OPTIMIZATION INVOLVING SEMI $E$-TYPE-I MAPS IN BANACH SPACES

inferred← citeshttps://doi.org/10.1504/ijor.2014.064019openalex-snapshot

Non-smooth multiobjective programming problem involving (dI - ρ - σ)-V-type I functions

inferred← citeshttps://doi.org/10.1515/jaa-2013-015openalex-snapshot

Nondifferentiable (Phi,rho)-type I and generalized (Phi,rho)-type I functions in nonsmooth vector optimization

inferred← citeshttps://doi.org/10.18576/amis/100313openalex-snapshot

Weak Pseudo-Invexity and Characterizations of Solutions in Multiobjective Programming

inferred← citeshttps://doi.org/10.2174/978160805110611001010119openalex-snapshot

Mixed Type Duality for Multiobjective Optimization Problems with Set Constraints

inferred← citeshttps://doi.org/10.22436/jnsa.012.11.06openalex-snapshot

E-optimality conditions and Wolfe E-duality for E-differentiable vector optimization problems with inequality and equality constraints

inferred← citeshttps://doi.org/10.2298/yjor130108025sopenalex-snapshot

On sufficiency in multiobjective programming involving generalized (G,C,ρ)-type I functions

inferred← citeshttps://doi.org/10.2989/16073606.2018.1509906openalex-snapshot

Duality models for multiobjective semiinfinite fractional programming problems involving type-I and related functions

inferred← citeshttps://doi.org/10.3934/jimo.2022004openalex-snapshot

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inferred← citeshttps://doi.org/10.3934/naco.2021014openalex-snapshot

$ V $-$ E $-invexity in $ E $-differentiable multiobjective programming

inferred← citeshttps://doi.org/10.3934/naco.2025024openalex-snapshot

Characterization techniques for optimal points in controlled variational models

inferred← citeshttps://doi.org/10.4134/ckms.2004.19.1.179openalex-snapshot

MULTIOBJECTIVE VARIATIONAL PROGRAMMING UNDER GENERALIZED VECTOR VARIATIONAL TYPE I INVEXITY

inferred← citeshttps://doi.org/10.4236/ajor.2011.14028openalex-snapshot

Optimality for Multi-Objective Programming Involving Arcwise Connected d-Type-I Functions

inferred← citeshttps://doi.org/10.4236/am.2011.24057openalex-snapshot

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