Necessary and sufficient conditions in constrained optimization
Mathematical Programming: Series A and B
Optimality conditions and duality in subdifferentiable multiobjective fractional programming
Journal of Optimization Theory and Applications
Optimality criteria and duality in multiple-objective optimization involving generalized invexity
Journal of Optimization Theory and Applications
Nonsmooth analysis and control theory
Nonsmooth analysis and control theory
Optimality conditions for Pareto nonsmooth nonconvex programming in Banach spaces
Journal of Optimization Theory and Applications
Optimization by Vector Space Methods
Optimization by Vector Space Methods
Generalized Invexity and Duality in Multiobjective Programming Problems
Journal of Global Optimization
Generalized Invexity and Duality in Multiobjective Programming Problems
Journal of Global Optimization
Duality in Vector Optimization in Banach Spaces with Generalized Convexity
Journal of Global Optimization
Multicriteria Optimization
Relative Pareto minimizers for multiobjective problems: existence and optimality conditions
Mathematical Programming: Series A and B
Computers & Mathematics with Applications
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In this paper, new results, which exhibit some new applications for Mordukhovich's subdifferential in nonsmooth optimization and variational problems, are established. Nonsmooth (fractional) multiobjective optimization problems in special Banach spaces are studied, and some necessary and sufficient conditions for weak Pareto-optimality for these problems are introduced. Through this work, we introduce into nonsmooth optimization theory in Banach algebras a new class of mathematical programming problems, which generalizes the notion of smooth KT-$(p,r)$-invexity. Some optimality conditions regarding the generalized KT-$(p,r)$-invexity notion and Kuhn-Tucker points are provided. Also, we seek a connection between linear (semi-) infinite programming and nonlinear programming. Some sufficient conditions for (proper) optimality under invexity are provided. A nonsmooth variational problem corresponding to a considered multiobjective problem is defined and the relations between the provided variational problem and the considered optimization problem are studied. The final part of the paper is devoted to illustrating a penalization mechanism, using the distance function as a tool, to provide some conditions to the solutions of the nonsmooth variational inequality problems. All results of the paper have been established in the absence of gradient vectors, using the properties of Mordukhovich's subdifferential in Asplund spaces.