A parallel stochastic method for solving linearly constrained concave global minimization problems

A parallel stochastic algorithm is presented for solving the linearly constrained concave global minimization problem. The algorithm is a multistart method and makes use of a Bayesian stopping rule to identify the global minimum with high probability. Computational results are presented for more than 200 problems on a Cray X-MP EA/464 supercomputer.

[1]  J. Ben Rosen,et al.  A parallel algorithm for constrained concave quadratic global minimization , 1988, Math. Program..

[2]  Alexander H. G. Rinnooy Kan,et al.  Bayesian stopping rules for multistart global optimization methods , 1987, Math. Program..

[3]  R. Horst,et al.  On the global minimization of concave functions , 1984 .

[4]  Panos M. Pardalos,et al.  A Collection of Test Problems for Constrained Global Optimization Algorithms , 1990, Lecture Notes in Computer Science.

[5]  Philip Wolfe,et al.  An algorithm for quadratic programming , 1956 .

[6]  Eric R. Zieyel Operations research : applications and algorithms , 1988 .

[7]  J. E. Falk,et al.  An Algorithm for Separable Nonconvex Programming Problems , 1969 .

[8]  A. Phillips,et al.  Parallel algorithms for constrained optimization , 1988 .

[9]  J. Mockus,et al.  The Bayesian approach to global optimization , 1989 .

[10]  Alexander H. G. Rinnooy Kan,et al.  Stochastic methods for global optimization , 1984 .

[11]  J. B. Rosen,et al.  Methods for global concave minimization: A bibliographic survey , 1986 .

[12]  Panos M. Pardalos,et al.  Constrained Global Optimization: Algorithms and Applications , 1987, Lecture Notes in Computer Science.

[13]  Pierre Hansen,et al.  An analytical approach to global optimization , 1991, Math. Program..

[14]  James E. Falk,et al.  A Successive Underestimation Method for Concave Minimization Problems , 1976, Math. Oper. Res..

[15]  J. Ben Rosen,et al.  Anomalous Acceleration in Parallel Multiple-Cost-Row Linear Programming , 1989, INFORMS J. Comput..

[16]  J. B. Rosen,et al.  A parallel algorithm for partially separable non-convex global minimization: Linear constraints , 1990 .

[17]  Alexander H. G. Rinnooy Kan,et al.  Concurrent stochastic methods for global optimization , 1990, Math. Program..

[18]  G. T. Timmer,et al.  Stochastic global optimization methods part I: Clustering methods , 1987, Math. Program..

[19]  Garth P. McCormick,et al.  Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems , 1976, Math. Program..