Solving constrained global optimization problems via a modified integral level-set method

This article proposes a modified level-set method for solving a constrained optimization problem. It first converts the problem into an equivalent unconstrained global optimization problem on a closed box via a non-smooth exact penalty function and then proposes a conceptual modified integral level-set method solving the equivalent optimization problem. To make the proposed method implementable, this article borrows the method of tossing points on a unit box via uniform distribution in number theory to generate and estimate level sets, with the error bounds of the integral of level sets being able to be estimated. Afterward, an implementable algorithm is proposed with its convergence proved. Several numerical examples show the efficiency of it.