We propose an algorithm for the global optimization of three problem classes: generalized semi-infinite, continuous coupled minimax and bi-level problems. We make no convexity assumptions. For each problem class, we construct an oracle that decides whether a given objective value is achievable or not. If a given value is achievable, the oracle returns a point with a value better than or equal to the target. A binary search is then performed until the global optimum is obtained with the desired accuracy. This is achieved by solving a series of appropriate finite minimax and min-max-min problems to global optimality. We use Laplace’s smoothing technique and a simulated annealing approach for the solution of these problems. We present computational examples for all three problem classes.

Generalized semi-infinite · Minimax · Bi-level · Globaloptimization · Min-max-min
Journal of Global Optimization
Department of Technology and Operations Management

Tsoukalas, A.T., Pistikopoulos, S, & Rustem, B. (2008). A Global Optimization Algorithm for Generalized Semi-Infinite, Continuous Minimax with Coupled Constraints and Bi-Level Problems. Journal of Global Optimization, 44, 235–253. Retrieved from http://hdl.handle.net/1765/134156