Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems

Tangential Extremal Principles for Finite and Infinite Systems of Sets, II: Applications to Semi-infinite and Multiobjective Optimization

This paper contains selected applications of the new tangential extremal principles and related results developed in Part I to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite programming and multiobjective optimization with countable constraint

Higher Order Duality for Vector Optimization Problem over Cones Involving Support Functions

In this paper, we consider a vector optimization problem over cones involving support functions in  objective as well as constraints and associate a unified higher order dual to it.  Duality result have been established under the conditions of higher order cone convex and related functions.  A number of previously studied problems appear as special cases. Keywords: Vector optimization, Cones, Support Functions, Higher Order Duality

Optimal control and nonlinear programming

In this thesis, we have two distinct but related subjects: optimal control and nonlinear programming. In the first part of this thesis, we prove that the value function, propagated from initial or terminal costs, and constraints, in the form of a differential equation, satisfy a subgradient form of the Hamilton-Jacobi equation in which the Hamiltonian is measurable with respect to time. In the second part of this thesis, we first construct a concrete example to demonstrate conjugate duality theory in vector optimization as developed by Tanino. We also define the normal cones corresponding to Tanino\u27s concept of the subgradient of a set valued mapping and derive some infimal convolution properties for convex set-valued mappings. Then we deduce necessary and sufficient conditions for maximizing an objective function with constraints subject to any convex, pointed and closed cone

Nondifferentiable G-Mond-Weir Type Multiobjective Symmetric Fractional Problem and Their Duality Theorems under Generalized Assumptions

[EN] In this article, a pair of nondifferentiable second-order symmetric fractional primal-dual model (G-Mond-Weir type model) in vector optimization problem is formulated over arbitrary cones. In addition, we construct a nontrivial numerical example, which helps to understand the existence of such type of functions. Finally, we prove weak, strong and converse duality theorems under aforesaid assumptions.Dubey, R.; Mishra, LN.; Sánchez Ruiz, LM. (2019). Nondifferentiable G-Mond-Weir Type Multiobjective Symmetric Fractional Problem and Their Duality Theorems under Generalized Assumptions. Symmetry (Basel). 11(11):1-18. https://doi.org/10.3390/sym11111348S118111