Nonlinear Programming--Sequential Unconstrained Minimization Techniques

Using Sequential Unconstrained Minimization Techniques to simplify SVM solvers

In this paper, we apply Sequential Unconstrained Minimization Techniques (SUMTs) to the classical formulations of both the classical L1 norm SVM and the least squares SVM. We show that each can be solved as a sequence of unconstrained optimization problems with only box constraints. We propose relaxed SVM and relaxed LSSVM formulations that correspond to a single problem in the corresponding up...

On the rate of convergence of sequential unconstrained minimization techniques

Iterative Reweighted Minimization Methods for $l_p$ Regularized Unconstrained Nonlinear Programming

In this paper we study general lp regularized unconstrained minimization problems. In particular, we derive lower bounds for nonzero entries of the firstand second-order stationary points and hence also of local minimizers of the lp minimization problems. We extend some existing iterative reweighted l1 (IRL1) and l2 (IRL2) minimization methods to solve these problems and propose new variants fo...

Alternating Minimization as Sequential Unconstrained Minimization: A Survey

Sequential unconstrained minimization is a general iterative method for minimizing a function over a given set. At each step of the iteration we minimize the sum of the objective function and an auxiliary function. The aim is to select the auxiliary functions so that, at least, we get convergence in function value to the constrained minimum. The SUMMA is a broad class of these methods for which...

Nonlinear complementarity as unconstrained and constrained minimization

The nonlinear complementarity problem is cast as an unconstrained minimization problem that is obtained from an augmented Lagrangian formulation. The dimensionality of the unconstrained problem is the same as that of the original problem, and the penalty parameter need only be greater than one. Another feature of the unconstrained problem is that it has global minima of zero at precisely all th...