Sparse principal component analysis (PCA) addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to interpret the principal components, and is applicable in a wide variety of fields including genetics and … Read more
We propose pivot methods that solve linear programs by trying to close the duality gap from both ends. The first method maintains a set $\B$ of at most three bases, each of a different type, in each iteration: a primal feasible basis $B^p$, a dual feasible basis $B^d$ and a primal-and-dual infeasible basis $B^i$. From … Read more
We investigate projected scaled gradient (PSG) methods for convex minimization problems. These methods perform a descent step along a diagonally scaled gradient direction followed by a feasibility regaining step via orthogonal projection onto the constraint set. This constitutes a generalized algorithmic structure that encompasses as special cases the gradient projection method, the projected Newton method, … Read more
Spectral functions of symmetric matrices — those depending on matrices only through their eigenvalues — appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their subdifferentials to the subdifferentials of their diagonal restrictions. This paper presents a new, short, and revealing derivation of this result. We then … Read more
In this paper, we consider the linearly constrained composite convex optimization problem, whose objective is a sum of a smooth function and a possibly nonsmooth function. We propose an inexact augmented Lagrangian (IAL) framework for solving the problem. The stopping criterion used in solving the augmented Lagrangian (AL) subproblem in the proposed IAL framework is … Read more
In this work, we present a new framework to increase effectiveness of metaheuristics in seeking good solutions for the general nonlinear optimization problem, called Cutting Box Strategy (CBS). CBS is based on progressive reduction of the search space through the use of intelligent multi-starts, where solutions already obtained cannot be revisited by the adopted metaheuristic. … Read more
When analyzing the relative performance of mutual funds, current data envelopment analysis (DEA) models with diversification only consider risks and returns over the entire investment process, which ignore the performance change in consecutive periods. This paper introduces a novel multi-period network DEA approach with diversification and the directional distance function. The new approach decomposes the … Read more
We investigate the asymptotic behavior of a stochastic version of the forward-backward splitting algorithm for finding a zero of the sum of a maximally monotone set-valued operator and a cocoercive operator in Hilbert spaces. Our general setting features stochastic approximations of the cocoercive operator and stochastic perturbations in the evaluation of the resolvents of the … Read more
We study sample average approximations under adaptive importance sampling. Based on a Banach-space-valued martingale strong law of large numbers, we establish uniform convergence of the sample average approximation to the function being approximated. In the optimization context, we obtain convergence of the optimal value and optimal solutions of the sample average approximation. CitationTechnical Report IEMS … Read more
The pooling problem is a nonconvex nonlinear programming problem (NLP) with applications in the refining and petrochemical industries, but also the coal mining industry. The problem can be stated as follows: given a set of raw material suppliers (inputs) and qualities of the supplies, find a cost-minimising way of blending these raw materials in intermediate … Read more