Partially Strictly Monotone and Nonlinear Penalty Functions for Constrained Mathematical Programs
Computational Optimization and Applications
Smooth Convex Approximation to the Maximum Eigenvalue Function
Journal of Global Optimization
A Unified Continuous Optimization Framework for Center-Based Clustering Methods
The Journal of Machine Learning Research
Penalty and Smoothing Methods for Convex Semi-Infinite Programming
Mathematics of Operations Research
A new augmented Lagrangian approach to duality and exact penalization
Journal of Global Optimization
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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.