NDLI: An approach to constrained global optimization based on exact penalty functions

Content Provider	Springer Nature Link
Author	Di Pillo, G. Lucidi, S. Rinaldi, F.
Copyright Year	2010
Abstract	In the field of global optimization many efforts have been devoted to solve unconstrained global optimization problems. The aim of this paper is to show that unconstrained global optimization methods can be used also for solving constrained optimization problems, by resorting to an exact penalty approach. In particular, we make use of a non-differentiable exact penalty function $${P_q(x;\varepsilon)}$$ . We show that, under weak assumptions, there exists a threshold value $${\bar \varepsilon >0 }$$ of the penalty parameter $${\varepsilon}$$ such that, for any $${\varepsilon \in (0, \bar \varepsilon]}$$ , any global minimizer of P $_{ q }$ is a global solution of the related constrained problem and conversely. On these bases, we describe an algorithm that, by combining an unconstrained global minimization technique for minimizing P $_{ q }$ for given values of the penalty parameter $${\varepsilon}$$ and an automatic updating of $${\varepsilon}$$ that occurs only a finite number of times, produces a sequence {x $^{ k }$} such that any limit point of the sequence is a global solution of the related constrained problem. In the algorithm any efficient unconstrained global minimization technique can be used. In particular, we adopt an improved version of the DIRECT algorithm. Some numerical experimentation confirms the effectiveness of the approach.
Starting Page	251
Ending Page	260
Page Count	10
File Format	PDF
ISSN	09255001
Journal	Journal of Global Optimization
Volume Number	54
Issue Number	2
e-ISSN	15732916
Language	English
Publisher	Springer US
Publisher Date	2010-07-15
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Nonlinear programming Global optimization Exact penalty functions DIRECT algorithm Real Functions Optimization Computer Science Operations Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Applied Mathematics Management Science and Operations Research Business, Management and Accounting Computer Science Applications

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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