Characterizations of Optimal Solution Set in Programming Problem under Inclusion Constrains

The optimal solution set of the interval linear programming problems

Determining the set of all optimal solutions of a linear program with interval data is one of the main problems discussed in interval optimization. We review two methods based on duality in linear programming, which are used to approximate the optimal set. Additionally, another decomposition method based on complementary slackness is proposed. This method provides the exact description of the o...

Characterizations of the solution set for quasiconvex programming in terms of Greenberg-Pierskalla subdifferential

In convex programming, characterizations of the solution set in terms of the subdifferential have been investigated by Mangasarian. An invariance property of the subdifferential of the objective function is studied, and as a consequence, characterizations of the solution set by any solution point and any point in the relative interior of the solution set are given. In quasiconvex programming, h...

Pareto Optimal Solution Analysis of Convex Multi-Objective Programming Problem

The main method of solving multi-objective programming is changing multi-objective programming problem into single objective programming problem, and then get Pareto optimal solution. Conversely, whether all Pareto optimal solutions can be obtained through appropriate method, generally the answer is negative. In this paper, the methods of norm ideal point and membership function are used to sol...

Characterizations of Asymptotic Cone of the Solution Set of a Composite Convex Optimization Problem

Characterizations of solution sets of cone-constrained convex programming problems

In this paper, we consider a type of cone-constrained convex program in finitedimensional space, and are interested in characterization of the solution set of this convex program with the help of the Lagrange multiplier. We establish necessary conditions for a feasible point being an optimal solution. Moreover, some necessary conditions and sufficient conditions are established which simplifies...