| Project/Area Number |
14550405
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
System engineering
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| Research Institution | MURORAN INSTITUTE OF TECHNOLOGY (2003)
Tokyo University of Science (2002) |
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Principal Investigator |
SHI Jianraing MURORAN INSTITUTE OF TECHNOLOGY, Department of Electrical and Electronic Engineering, Associate Professor, 工学部, 助教授 (70287465)
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| Co-Investigator(Kenkyū-buntansha) |
降籏 徹馬 東京理科大学, 経営学部, 助手 (80287466)
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| Project Period (FY) |
2002 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,800,000 (Direct Cost: ¥1,800,000)
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| Keywords | fractional programming / convex function / global optimization / dual problem / algorithm / reverse convex set / trust-region / d.c.set and d.c.function / 逆凸 / d.c. / fractional programming / sum-of-ratios problem / global optimization / branch-and-bound algorithm |
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| Research Abstract |
We give a summary of our research results in order of papers published within the term of project, respectively. In [1], we present some algorithms for solving convex maximization problems with some fuzzy constraints. We transform the reverse convex feasible region to a d.c.set, then solve the problem by combining the techniques of d.c.method and on-line vertices enumeration method. In [2]we develop two algorithms for globally optimizing a special class of linear programs with an additional concave constraint. We assume that the concave constraint is defined by a separable concave function. Exploiting this special structure, we apply Falk-Soland's branch-and-bound algorithm for concave minimization in both direct and indirect manners. In [3]we consider : max_x _<∈D>{Σ_<mj=1> g_j(x)/h_j(x)}, where g_j(x) >=0 and h_j(x)>0,j=1, triple bond,m are d.c.functions over a convex compact set D in R^n. Several favorable properties are developed and a branch-and-bound algorithm based on the conical partition and the outer approximation scheme is presented. In [4]we are concerned with a nondifferentiable minimax fractional programming problem. We derive a Kuhn-Tucker type sufficient optimality condition for an optimal solution to the problem and establish week, strong and converse duality theorems for the problem and its three different forms of dual problems. The results in this paper extend a few known results in the literature. In [5]A trust-region algorithm is presented for solving optimization problem with equality constraints. The algorithm uses the Byrd-Omojokun scheme to compute the steps, and decompose the trial steps into two components : normal component and tangential component. But it differs from the Byrd-Omojokun algorithm with a reduced dimension approach in computing each tangential component. Global convergence of the proposed algorithm is proved under some mild assumptions.
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