Logarithmic Barrier Optimization Problem Using Neural Network

TL;DR

This paper proposes a neural network-based approach using a logarithmic barrier function to approximately solve linearly constrained continuous optimization problems, with an algorithm ensuring convergence as the barrier parameter decreases.

Contribution

It introduces a novel neural network algorithm employing a logarithmic barrier function for solving constrained optimization problems with proven convergence properties.

Findings

Developed an algorithm generating a decreasing solution sequence.

Demonstrated convergence of solutions as barrier parameter approaches zero.

Applied the method to linear constrained optimization problems.

Abstract

The combinatorial optimization problem is one of the important applications in neural network computation. The solutions of linearly constrained continuous optimization problems are difficult with an exact algorithm, but the algorithm for the solution of such problems is derived by using logarithm barrier function. In this paper we have made an attempt to solve the linear constrained optimization problem by using general logarithm barrier function to get an approximate solution. In this case the barrier parameters behave as temperature decreasing to zero from sufficiently large positive number satisfying convexity of the barrier function. We have developed an algorithm to generate decreasing sequence of solution converging to zero limit.