Bregman distance optimization techniques for constrained decision-making problems in engineering systems

Abstract

Inefficient optimization procedures should be used for constrained decision-making in engineering systems in order to provide efficient solution for nonlinear constraints, dynamic nature of the process, and multiple objectives. Traditional optimization procedures often suffer from limitations in adaptiveness and preserving feasibility through iterative updating of solution. This research proposes Bregman Distance Optimization approach to solve the problem of constrained decision-making in engineering systems based on the use of adaptive distance functions constructed by means of strictly convex functions. This technique uses Bregman projection, Bregman proximal point optimization, and mirror descent in order to ensure stability and convergence of the solution while preserving the constraints of the system. The suggested approach solves the problems of constrained optimization using Legendre kernel and evaluates its performance in the case of simplex, box, and positive definite matrix constraints. The analysis provides convergence properties such as projection uniqueness, generalized Pythagorean inequality, and explicit convergence rates. Evaluation of the technique using maintenance-budget allocation problem shows that the value of the objective function is decreased from 0.0961 to 0.0223 within five iterations and the feasible decision variable. This proves that Bregman distance optimization is more adaptable, computationally efficient, and capable of preserving constraints than the traditional distance optimization procedure.