An exact penalty function method for nonlinear mixed discrete programming problems

In this paper, we consider a general class of nonlinear mixed discrete programming problems. By introducing continuous variables to replace the discrete variables, the problem is first transformed into an equivalent nonlinear continuous optimization problem subject to original constraints and additi...

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Vydané v:Optimization letters Ročník 7; číslo 1; s. 23 - 38
Hlavní autori: Yu, Changjun, Teo, Kok Lay, Bai, Yanqin
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer-Verlag 01.01.2013
Predmet:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
Nonlinear mixed integer programming
Exact penalty function
ISSN:1862-4472, 1862-4480
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Popis
Shrnutí:In this paper, we consider a general class of nonlinear mixed discrete programming problems. By introducing continuous variables to replace the discrete variables, the problem is first transformed into an equivalent nonlinear continuous optimization problem subject to original constraints and additional linear and quadratic constraints. Then, an exact penalty function is employed to construct a sequence of unconstrained optimization problems, each of which can be solved effectively by unconstrained optimization techniques, such as conjugate gradient or quasi-Newton methods. It is shown that any local optimal solution of the unconstrained optimization problem is a local optimal solution of the transformed nonlinear constrained continuous optimization problem when the penalty parameter is sufficiently large. Numerical experiments are carried out to test the efficiency of the proposed method.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-011-0391-2