A new minimax algorithm and its application to optics problems

Minimax problems arise in various applications. The structure of certain minimax problems has long been useful in designing algorithms for their solution. The structure of finite minimax problems can be exploited within the context of primal-dual interior-point methods. A new algorithm has been designed which implements this technique. A log-barrier penalty function is utilized, with convergence assured by the use of a trust-region method. Iterates are chosen which take into account the special form of minimax problems. Dual variables are chosen to encourage the development of the minimax structure. It is shown that any limit points of the developed algorithm are second-order optima of the minimax problem. Numerical results are presented which indicate the efficacy of this approach.; Several optics problems dealing with layered dielectrics can be cast as minimax problems. It is shown how these formulations are derived. In planar geometry we have the problem of optimal design of transparent and reflective laminations. In cylindrical geometry the problem becomes that of designing a low-loss optical cable. Numerical results for several cases are presented. These indicate that great advancements can be made by designing optical devices with minimax techniques.