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.

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