Enhanced Pattern Search Combined with Filter Method for Solving Nonlinear Bilevel Programming Problems

This paper introduces an innovative approach that combines the traditional filter method with an enhanced pattern search method specifically designed to solve nonlinear bilevel programming problems (BLPP) with a convex lower-level problem. The enhanced pattern search method incorporates a novel mesh that utilizes Karush-Kuhn-Tucker (KKT) conditions of the lower-level problem to effectively navigate the solution space. In this approach, the KKT multiplier is treated as an auxiliary variable and is computed through parametric goal programming. Through several numerical experiments and detailed computational analysis, we demonstrate that the enhanced pattern search method provides more accurate estimations of constraint violations, leading to more effective and efficient attainment of optimal solutions with reduced computation time compared to existing methods.