A Research on Practical Algorithms for Geometrical Optimization Problems with Nonconvex Structure
Project/Area Number  05650061 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
Engineering fundamentals

Research Institution  University of Tsukuba 
Principal Investigator 
KUNO Takahito Institute of Information Sciences and Electronics, University of Tsukuba Associate Professor, 電子・情報光学系, 助教授 (00205113)

Project Fiscal Year 
1993 – 1994

Project Status 
Completed(Fiscal Year 1994)

Budget Amount *help 
¥1,600,000 (Direct Cost : ¥1,600,000)
Fiscal Year 1994 : ¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1993 : ¥700,000 (Direct Cost : ¥700,000)

Keywords  Mathematical Programming / Global optimization / Nonconvex function / Computational Geometry / Algorithm / 数理計画法 / 最適化 / 非凸関数 / 計算幾何学 / アルゴリズム 
Research Abstract 
In this research, we studied some practical algorithme for solving certain classes of geometrical optimization problems with nonconvex structure. We applied global optimization techniques to the problems in the plane and constructed some algorithms for obtaining a globally optimal solution. A few of the results are as follows : 1.Globally optimization of ranktwo reverse convex programs : We proposed an algorithm for solving reverse convex program which contains a quasiconcave constraint function defined by two linearly independent ndimensional vectors. The computational experiments indicated that the algorithm can generate globally optimal solutions very efficiently compared with any existing algorithms. 2.Globally minimization of ranktwo saddle functions on a polytope : We proposed an algorithm for minimizing a composite function of a twodimensional saddle function and ndimensional affine functions. The computational experiments indicated that the algorithm solves fairly large scale problems. In addition to the above problems, we studied a class of nonconvex network optimization problems. To solve the problems efficiently, we used computational geometry as some procedures of the algorithm. As a result, we obtained the following : 3.Globally optimization of productiontransportation problems : We proposed a pseudopolynomialtime algorithm for solving a class of productiontransportation problem. All the above mentioned algorithms decompose a given problem into several convex subproblems. This solution strategy can also be applied to many other classes of optimization problems.

Report
(4results)
Research Output
(19results)