A Sequential Algorithm for Sampled Mixed-integer Optimization Problems

Abstract

In this paper, we propose a computationally efficient algorithm for solving mixed-integer sampled optimization problems involving a large number of constraints. The proposed algorithm has a sequential nature. Specifically, at each iteration of the algorithm, the feasibility of a candidate solution is verified for all the constraints involved in the sampled optimization problem and violating constraints are identified. As a second step, an optimization problem is formed whose constraint set involves the current basis—the minimal set of constraints defining the current candidate solution—and a limited number of the observed violating constraints. We prove that the algorithm converges to the optimal solution in finite time. Additionally, we establish the effectiveness of the proposed algorithm using mixed-integer linear, and quadratically constrained quadratic programming problems.