On semidifferentiable interval-valued programming problems

Kin Keung Lai,Shashi Kant Mishra,Avanish Shahi

doi:10.1186/s13660-021-02566-2

Kin Keung Lai, Shashi Kant Mishra + Show 1 more

Open Access

https://doi.org/10.1186/s13660-021-02566-2

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Abstract

In this paper, we consider the semidifferentiable case of an interval-valued minimization problem and establish sufficient optimality conditions and Wolfe type as well as Mond–Weir type duality theorems under semilocal E-preinvex functions. Furthermore, we present saddle-point optimality criteria to relate an optimal solution of the semidifferentiable interval-valued programming problem and a saddle point of the Lagrangian function.

Highlights

The technique of solving optimization problems has wide applications in many research areas
Paper [3] dealt with two types of solutions for an interval-valued optimization problem and established the Karush–Kuhn–Tucker optimality conditions
We present some sufficient optimality conditions for (IVP)

Summary

Introduction

The technique of solving optimization problems has wide applications in many research areas. 3, we establish sufficient optimality conditions for interval-valued programming using E-η-semidifferentiable and semilocal E-preinvex functions. Theorem 4.1 (Weak duality) Let xand (z, wL, wU , τ ) be the feasible solutions to (IVP) and (IVWD), respectively, with E(z) = z. L, such that w L dFL + x; η E x , x + w U dFU + x; η E x , xl and τjgj(x) = 0 j=1 show that (x, w L, w U , τ) is a feasible solution to (IVWD) and the analogous objective values are the same. Theorem 4.3 (Strict converse duality) Let xand (z, w L, w U , τ) be the feasible solutions to (IVP) and (IVWD), respectively, with E(z) = z.

Mond–Weir type duality Consider the following Mond–Weir type dual model:

Conclusions