A unified approach to nonconvex programming problems using branchandbound algorithms
Project/Area Number 
13680505

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
社会システム工学

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

CoInvestigator(Kenkyūbuntansha) 
YOSHISE Akiko Univesity of Tsukuba, Institute of Policy and Planning Sciences, Associate Professor, 社会工学系, 助教授 (50234472)

Project Period (FY) 
2001 – 2002

Project Status 
Completed (Fiscal Year 2002)

Budget Amount *help 
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2002: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2001: ¥2,100,000 (Direct Cost: ¥2,100,000)

Keywords  Global optimization / nonconvex program / branchandbound method / mathematical programming / algorithm 
Research Abstract 
We made a study mainly on three classes of nonconvex optimization problems, each of which is abundant in applications to realworld social systems : (1) In almost every optimization problem, both objective and constraint functions can be written as the difference of two convex functions. Using this property, the problem can be transformed into a convex minimization problem with an additional reverse convex constraint. We proposed three branchandbound algorithms for solving this kind of nonconvex optimization problems. We showed that each algorithm generates a globally optimal solution in finite iterations if the reverse convex constraint function is separable. (2) The sumofratios problem is a problem, of minimizing a sum of linear rations over a convex set, and is known to be intractable. We devised an inexpensive procedure for computing a tignt lower bound on the optical value. We incorporated it into a branchandbound algorithm and succeeded in solving the problem much faster than the existing algorithms. (3) Many of chemical process design problems can be formulated as optimization problems but highly nonconvex ones, say mixedinteger nonlinear programming problems. To solve this kind of problems, we proposed a hybrid algorithm of brandandbound and revised general benders decomposition methods. We then proved that the algorithm certainly converges to globally optimal solutions for some typical chemical process design problems. Each of the proposed algorithms is based on the idea of branch and bound. To execute the bounding operations efficiently, we also studied an interiorpoint algorithm for solving relaxed problems.

Report
(3 results)
Research Products
(11 results)