Journal of Global Optimization
Partially Strictly Monotone and Nonlinear Penalty Functions for Constrained Mathematical Programs
Computational Optimization and Applications
Interval optimization for uncertain structures
Finite Elements in Analysis and Design
Numerical Comparison of Augmented Lagrangian Algorithms for Nonconvex Problems
Computational Optimization and Applications
Combined SVM-Based Feature Selection and Classification
Machine Learning
Blind Source Separation by Sparse Decomposition in a Signal Dictionary
Neural Computation
Nonlinear Rescaling as Interior Quadratic Prox Method in Convex Optimization
Computational Optimization and Applications
Convergence of Successive Approximation Methods with Parameter Target Sets
Mathematics of Operations Research
Local convergence of an augmented Lagrangian method for matrix inequality constrained programming
Optimization Methods & Software
Intensity modulated radiotherapy treatment planning by use of a barrier-penalty multiplier method
Optimization Methods & Software
Primal-dual exterior point method for convex optimization
Optimization Methods & Software
Unified theory of augmented Lagrangian methods for constrained global optimization
Journal of Global Optimization
Optimal call admission control for an IEEE 802.16 wireless metropolitan area network
NET-COOP'07 Proceedings of the 1st EuroFGI international conference on Network control and optimization
Inexact Proximal Point Methods for Variational Inequality Problems
SIAM Journal on Optimization
A class of nonlinear Lagrangians for nonconvex second order cone programming
Computational Optimization and Applications
Robust solutions of uncertain linear programs
Operations Research Letters
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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.