Global Optimal Solution to Discrete Value Selection Problem with Inequality Constraints

TL;DR

This paper introduces a canonical dual approach to solve quadratic discrete value selection problems with inequality constraints, transforming them into a continuous concave maximization problem, and demonstrates its effectiveness through numerical simulations.

Contribution

It develops a novel canonical dual method that converts a quadratic discrete problem with inequalities into a solvable continuous concave maximization problem.

Findings

Effective solution for large-scale problems

Demonstrates efficiency of the dual approach

Applicable to various inequality-constrained discrete problems

Abstract

This paper presents a canonical dual method for solving a quadratic discrete value selection problem subjected to inequality constraints. The problem is first transformed into a problem with quadratic objective and 0-1 integer variables. The dual problem of the 0-1 programming problem is thus constructed by using the canonical duality theory. Under appropriate conditions, this dual problem is a maximization problem of a concave function over a convex continuous space. Numerical simulation studies, including some large scale problems, are carried out so as to demonstrate the effectiveness and efficiency of the method proposed.