NDLI: Penalty and Barrier Methods: A Unified Framework

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Auslender, A.
Copyright Year	1999
Abstract	It is established that many optimization problems may be formulated in terms of minimizing a function $x\rightarrow f_0 (x) + H_\infty (f_1 (x), f_2 (x),\ldots,f_m (x)) + L_\infty (Ax-b)$, where the $f_i$ are closed functions defined on $\mathbb{R}^N$, and where $H_\infty$ and $L_\infty$ are the recession functions of closed, proper, convex functions H and L. A is a linear transformation from $\mathbb{R}^N$ to a finite dimensional vector space Y with $b\in Y$. A generic algorithm, based on the properties of recession functions, is proposed. This algorithm not only encompasses almost all penalty and barrier methods in nonlinear programming and in semidefinite programming, but also generates new types of methods. Primal and dual convergence theorems are given.
Starting Page	211
Ending Page	230
Page Count	20
File Format	PDF
ISSN	10526234
DOI	10.1137/S1052623497324825
e-ISSN	10957189
Journal	SIAM Journal on Optimization (SJOPE8)
Issue Number	1
Volume Number	10
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-31
Access Restriction	Subscribed
Subject Keyword	semidefinite programming convex and nonlinear programming Eigenvalues, eigenvectors Linear programming Programming in abstract spaces penalty and barrier methods Convex programming Sensitivity, stability, parametric optimization
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Software

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