GLOPT - A Program for Constrained Global Optimization

Abstract. GLOPT is a Fortran77 program for global minimization of a blockseparable objective function subject to bound constraints and block-separable constraints. It finds a nearly globally optimal point that is near a true local minimizer. Unless there are several local minimizers that are nearly global, we thus find a good approximation to the global minimizer. GLOPT uses a branch and bound technique to split the problem recursively into subproblems that are either eliminated or reduced in their size. This is done by an extensive use of the block separable structure of the optimization problem. In this paper we discuss a new reduction technique for boxes and new ways for generating feasible points of constrained nonlinear programs. These are implemented as the first stage of our GLOPT project. The current implementation of GLOPT uses neither derivatives nor simultaneous information about several constraints. Numerical results are already encouraging. Work on an extension using curvature information and quadratic programming techniques is in progress. Key words: global optimization, global minimum, branch and bound, block separable, feasibility, tunneling, reduce 1991 MSC codes: primary 90C26; secondary 65K05 1. Generalities Optimization is one of the basic mathematical techniques that lie at the heart of modern competitive management, design and development. The oldest and best developed part, linear programming, is an indispensable planning tool once the interrelations of tasks is complex enough. Aircraft scheduling, the structural design of buildings or bridges, the design of chemical production plants, the operation of electric power plants, the analysis of electrical circuits, and many other problems can, however, be modeled only through nonlinear relationships. Except in special circumstances, this introduces the potentiality of multiple minima, and in many cases, such multiple minima are indeed known to occur. The optimum is in this case the global minimum. The Global Optimization Home Page on the World Wide Web (WWW) wit