A Block-Alternating Iterative Approach for a Class of Non-Convex Optimization Problems

TL;DR

This paper introduces a block-alternating iterative method for non-convex optimization problems common in control applications, reformulating them into convex subproblems to improve convergence and computational efficiency.

Contribution

It presents a novel iterative approach that decomposes non-convex problems into convex subproblems, with theoretical convergence guarantees and a practical Python implementation.

Findings

Method converges reliably to local minima in control problems.

Numerical and real-world examples demonstrate effectiveness.

Python platform facilitates comparison with existing algorithms.

Abstract

Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs. To address this challenge, this paper proposes a novel block-alternating iterative method that decomposes the original problem into variable-specific subproblems, which are solved iteratively. Under the assumption that the problem is convex with respect to each decision variable, the proposed approach reformulates the original problem into a sequence of convex subproblems. Theoretical results are established regarding the convergence and optimality of the method. In addition, a numerical example and a real-world control engineering application are presented to demonstrate its effectiveness. Finally, this paper introduces a ready-to-use Python platform that implements the proposed method, together with existing algorithms, to facilitate comparison and adoption.