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On Multi-objective Optimization Problems and Vector Variational-Like Inequalities
This paper deals with nonsmooth multi-objective optimization problems involving locally Lipschitz \(V-r\)-invexity using Michel–Penot...
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Second-order strong optimality and duality for nonsmooth multiobjective fractional programming with constraints
This paper investigates nonsmooth multiobjective fractional programming (NMFP) with inequalities and equalities constraints in real reflexive Banach...
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Generalized Invexity and Generalized Invariant Monotonicity
A closely related concept of the convexity of a real-valued function is the monotonicity of a vector-valued function. It is well known that the...
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Constraint Qualifications and Optimality Criteria for Nonsmooth Multiobjective Programming Problems on Hadamard Manifolds
This article deals with a class of constrained nonsmooth multiobjective programming problems (NMOPP) in the setting of Hadamard manifolds. The...
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Optimality Conditions for Minimax Optimization Problems with an Infinite Number of Constraints and Related Applications
This paper is concerned with the study of optimality conditions for minimax optimization problems with an infinite number of constraints, denoted by...
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Historical steps of development of convexity as a field
In this chapter we will show historical steps of the development of convexity as a field and, in addition, developments of the relations between...
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On a New Class of Interval-Valued Variational Control Problems
A class of optimization problems that includes interval-valued multiple integral objective functionals is investigated in this paper. First, a new...
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Optimality conditions and duality for continuous-time programming with multiple interval-valued objective functions
The objective of this paper is to study the interval-valued multiobjective continuous-time programming. First, both Karush–Kuhn–Tucker necessary and...
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Deep Learning Optimization
In Chap. 6 , we discussed various optimization methods for deep neural network training. Although...
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Fractional variational duality results for higher-order multiobjective problems
This paper provides a study of multiobjective fractional variational programs involving support functions. It then explains the concept of...
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Characterization results of solutions in interval-valued optimization problems with mixed constraints
In this paper, we establish some characterization results of solutions associated with a class of interval-valued optimization problems with mixed...
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On constrained set-valued optimization problems with \(\rho \)-cone arcwise connectedness
In this paper, we establish the sufficient Karush–Kuhn–Tucker (for short, KKT) conditions of a set-valued optimization problem (P) via contingent...
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Duality Results for Fractional Variational Problems and Its Application
This article is tendered to discuss the nondifferentiable class of multiobjective variational problems of minimizing a vector of quotients of...
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Hanson-Antczak-Type Generalized V-Invexity I
In this chapter, based on [1], numerous sets of global parametric sufficient efficiency conditions under various Hanson-Antczak-type generalized...
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Duality theorems for nondifferentiable semi-infinite interval-valued optimization problems with vanishing constraints
In this paper, we study the duality theorems of a nondifferentiable semi-infinite interval-valued optimization problem with vanishing constraints...
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Convex functions
Convex functions and convex sets are somewhat interdependent. When studying convex sets, some convex functions play a very important role (mainly the...
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On semidifferentiable interval-valued programming problems
In this paper, we consider the semidifferentiable case of an interval-valued minimization problem and establish sufficient optimality conditions and...
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Introduction
Optimization problems are as old as science itself, implicit in the behavior of humanity. These are defined by their specific objective functions,...