1992 Fiscal Year Final Research Report Summary
Global Minimization of Nonconvex Functions and Its Applications to Social Systems
| Project/Area Number |
03832018
|
|---|
| Research Category |
Grant-in-Aid for General Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
社会システム工学
|
|---|
| Research Institution | Tokyo Institute of Technology |
|---|
Principal Investigator |
KONNO Hiroshi Tokyo Institute of Technology, Inst. of Human & Social Sci., Professor, 工学部, 教授 (10015969)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
PHAN Thien thach Tokyo Institute of Technology, Inst. of Human & Social Sci., Asst. Professor., 工学部, 助手 (10242299)
YAJIMA Yasutoshi Tokyo Institute of Technology, Dept. of IE & Management Int., Asst. Professor., 工学部, 助手 (80231645)
KUNO Takahito Univ. of Tsukuba Inst. of Electronics & Inf. Sci., Asst. Professor. (00205113)
|
|---|
| Project Period (FY) |
1991 – 1992
|
| Keywords | Global optimization / Nonconvex minimization / Outer approximation method / Parametrization / Convex mulitiplicative program / Bilinear programming problem / Nonconvex duality / Average polynomial order algorithm |
|---|
| Research Abstract |
In 1989, we succeeded in solving the minimization problem of a product of two affine functions on a polytope. This result was soon extended to the minimization of a sum and a product of two fractional functions. The key idea behind these algorithms is the combination of parametrization and outer approximation. We extended this approach to several other global optimization problems including (a) minimization of the product of several convex functions, (b) minimization of a generalized convex multiplicative functions, (c) lower rank bilinear programming problems, (d) minimization of a convex function subject to linear multiplicative constraints. Also, we proved a surprising result that the algorithm for (c) is a an average-polynomial order algorithm. Also, we applied the result of (c) to a class of problems in computational geometry. In addition, we proposed (e) a decomposition algorithm for a class of global optimization problems with a decomposable structure, (f) an outer approximation algorithm for d.c. programming problems with low nonconvexity rank.
Further, we studied mathematical structures of global optimization problems. Some of the important results are (g) duality theory for d.c. programming problems, and (h) degree of nonconvexity of nonconvex functions and nonconvex sets in Hilbert space.
|
