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Zbl 0872.90068
Ben-Tal, Aharon; Zibulevsky, Michael
Penalty/Barrier multiplier methods for convex programming problems. (English)
[J] SIAM J. Optim. 7, No.2, 347-366 (1997). ISSN 1052-6234; ISSN 1095-7189/e

Summary: We study a class of methods for solving convex programs, which are based on nonquadratic augmented Lagrangians for which the penalty parameters are functions of the multipliers. This gives rise to Lagrangians which are nonlinear in the multipliers. Each augmented Lagrangian is specified by a choice of a penalty function $\varphi$ and a penalty-updating function $\pi$. The requirements on $\varphi$ are mild and allow for the inclusion of most of the previously suggested augmented Lagrangians. More importantly, a new type of penalty/barrier function (having a logarithmic branch glued to a quadratic branch) is introduced and used to construct an efficient algorithm. Convergence of the algorithms is proved for the case of $\pi$ being a sublinear function of the dual multipliers. The algorithms are tested on large-scale quadratically constrained problems arising in structural optimization.

MSC 2000:: *90C25 Convex programming
74P99 Optimization solid mechanics
90C90 Appl. of mathematical programming

Keywords: nonquadratic augmented Lagrangians; penalty function; convergence; structural optimization

Cited in: Zbl 1170.90529 Zbl 1039.90053

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