NDLI: On the behavior of first-order penalty methods for conic constrained convex programming when Lagrange multipliers do not exist

Content Provider	IEEE Xplore Digital Library
Author	Necoara, Ion Patrascu, Andrei
Copyright Year	2015
Description	Author affiliation: Automatic Control and Systems Engineering Department, University Politehnica Bucharest, Romania (Necoara, Ion; Patrascu, Andrei)
Abstract	In this paper we analyze the numerical behavior of first-order quadratic penalty methods for solving large-scale conic constrained convex problems with composite objective function. Contrary to the most of the results on penalty methods, in this work we do not assume the existence of a finite optimal Lagrange multiplier. We derive the iteration complexity of the classical quadratic penalty method, where the corresponding penalty regularized formulation of the original problem is solved using Nesterov's fast gradient algorithm. We provide rate of convergence results in terms of feasibility violation and suboptimality for adaptive and non-adaptive variants of the penalty scheme, under various assumptions on the composite objective function. Finally, we show on a simple example that our complexity estimates are tight.
Starting Page	1378
Ending Page	1383
File Size	192857
Page Count	6
File Format	PDF
e-ISBN	9781479978861
DOI	10.1109/CDC.2015.7402403
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-12-15
Publisher Place	Japan
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Linear programming Complexity theory Optimization Convergence Convex functions Programming Signal processing algorithms
Content Type	Text
Resource Type	Article

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