Penalty Methods

Alexander J. Zaslavski
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Alexander J. Zaslavski: The Technion – Israel Institute of Technology

Chapter Chapter 15 in Numerical Optimization with Computational Errors, 2016, pp 239-264 from Springer

Abstract: Abstract In this chapter we use the penalty approach in order to study constrained minimization problems in infinite dimensional spaces. A penalty function is said to have the exact penalty property if there is a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem. Since we consider optimization problems in general Banach spaces, not necessarily finite-dimensional, the existence of solutions of original constrained problems and corresponding penalized unconstrained problems is not guaranteed. By this reason we deal with approximate solutions and with an approximate exact penalty property which contains the classical exact penalty property as a particular case. In our recent research we established the approximate exact penalty property for a large class of inequality-constrained minimization problems. In this chapter we improve this result and obtain an estimation of the exact penalty.

Keywords: Exact Penalty Property; Inequality Constrained Minimization Problems; Penalty Approach; Penalty Coefficient; Introduce Penalty Functions (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-30921-7_15

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DOI: 10.1007/978-3-319-30921-7_15

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