Optimality and duality for complex multi-objective programming

<p style='text-indent:20px;'>We consider a complex multi-objective programming problem (CMP). In order to establish the optimality conditions of problem (CMP), we introduce several properties of optimal efficient solutions and scalarization techniques. Furthermore, a certain parametric dual model is discussed, and their duality theorems are proved.</p>

ON OPTIMALITY AND DUALITY IN INTERVAL-VALUED VARIATIONAL PROBLEM WITH B-(p,r)-INVEXITY

In this paper, we consider a class of interval-valued variational optimization problem. We extend the definition of B -( p,r )- invexity which was originally defined for scalar optimization problem to the interval-valued variational problem. The necessary and sufficient optimality conditions for the problem have been established under B -( p,r )-invexity assumptions. An application, showing utility of the sufficiency theorem in real-world problem, has also been provided. In addition to this, for an interval- optimization problem Mond-Weir and Wolfe type duals are presented and related duality theorems have been proved. Non-trivial examples verifying the results have also been presented throughout the paper.

Optimality and duality for nonsmooth semi-infinite mathematical program with equilibrium constraints involving generalized invexity of order σ > 0

In this paper, we derive sufficient condition for global optimality for a nonsmooth semi-infinite mathematical program with equilibrium constraints involving generalized invexity of order σ > 0 assumptions. We formulate the Wolfe and Mond-Weir type dual models for the problem using convexificators. We establish weak, strong and strict converse duality theorems to relate the semi-infinite mathematical program with equilibrium constraints and the dual models in the framework of convexificators.

Optimality and duality for nonsmooth semi-infinite E-convex multi-objective programming with support functions

In this paper, we study a nonsmooth semi-infinite multi-objective E-convex programming problem involving support functions. We derive sufficient optimality conditions for the primal problem. We formulate Mond-Weir type dual for the primal problem and establish weak and strong duality theorems under various generalized E-convexity assumptions.