Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.8.2024.2.01

Volume 8, Issue 2, 1 April 2024, Pages 181-197

 

Abstract. Outer approximation (OA) for solving convex mixed-integer nonlinear programming (MINLP) problems is heavily dependent on the convexity of functions and a natural issue is to relax the convexity assumption. This paper is devoted to OA for dealing with a pseudo-convex MINLP problem. By solving a sequence of nonlinear subproblems, we use Lagrange multiplier rules via Clarke subdifferentials of subproblems to introduce a parameter and then equivalently reformulate such MINLP as the mixed-integer linear program (MILP) master problem. Then, an OA algorithm is constructed to find the optimal solution to the MNILP by solving a sequence of MILP relaxations. The OA algorithm is proved to terminate after a finite number of steps. Numerical examples are illustrated to test the constructed OA algorithm.

 

How to Cite this Article:
Z. Wei, L. Chen, J.C. Yao, Outer approximation for pseudo-convex mixed-integer nonlinear program problems, J. Nonlinear Var. Anal. 8 (2024), 181-197.