Research on Global Optimization Problems in Engineering Systems

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Main reuslts of this research project are the following.(1)We proposed a type of lexicographic ordering method to prevent possible convergence of the outer-approximation method to a point x^<**> epsilon^P where P is the set of Pareto optimal solution associated with a minimization of a convex function on P.We are now able to obtain a solution on P without fail by using this new method.(2)We developed an outer approximation method for a concave cost production-transportation network and demonstrated its efficiency for low rank problems, namely, problems containing relatively few concave cost arcs.(3)We developed an efficint algorithm for solving low rank concave quadratic programming problems by using Rosen's cutting plane and Tuy's cutting plane method. This method is very efficient and we may be able to obtain an even more efficient method by combining it with a heuristic such as tabusearch approach.(4)Konno wrote a survey article on low rank global optimization problems, which was published in Joho-Shori.(5)Completed a monograph entitled "Optimization on Low Rank Nonconvex Structures" to be published from Kluwer Academic Publishers in 1996. This book is based upon about 100 papers published by Konno, Thach, Tuy, Kuno and Yajima in the past 10 years.