Application of Sequential Unconstrained Minimization Technique to LMFBR Core Design Optimization Problem

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...

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

New Sequential and Parallel Derivative-Free Algorithms for Unconstrained Minimization

This paper presents sequential and parallel derivative-free algorithms for finding a local minimum of smooth and nonsmooth functions of practical interest. It is proved that, under mild assumptions, a sufficient decrease condition holds for a nonsmooth function. Based on this property, the algorithms explore a set of search directions and move to a point with a sufficiently lower functional val...

Sensitivity Computation of the L1 Minimization Problem and Its Application to Dictionary Design Sensitivity Computation of the 1 Minimization Problem and Its Application to Dictionary Design

Recently, there has been a growing interest in application of sparse representation for inverse problems. Most studies have concentrated in devising ways for sparse representation of a solution using a given prototype dictionary. Very few studies have addressed the more challenging problem of constructing an optimal dictionary, and even these were primarily devoted to the simplistic sparse codi...