We consider the alternating proximal gradient method (APGM) proposed to solve a convex minimization model with linear constraints and separable objective function which is the sum of two functions without coupled variables. Inspired by Peaceman-Rachford splitting method (PRSM), a nature idea is to extend APGM to the symmetric alternating proximal gradient method (SAPGM), which can … Read more
In this work we consider the feature ranking problem where, given a set of training instances, the task is to associate a score to the features in order to assess their relevance. Feature ranking is a very important tool for decision support systems, and may be used as an auxiliary step of feature selection to … Read more
In this paper we propose a new way to compute a warm starting point for a challenging global optimization problem related to Earth imaging in geophysics. The warm start consists of a velocity model that approximately solves a full-waveform inverse problem at low frequency. Our motivation arises from the availability of massively parallel computing platforms … Read more
In this paper, we consider the tensor generalized eigenvalue complementarity problem (TGEiCP), which is an interesting generalization of matrix eigenvalue complementarity problem (EiCP). First, we given an affirmative result showing that TGEiCP is solvable and has at least one solution under some reasonable assumptions. Then, we introduce two optimization reformulations of TGEiCP, thereby beneficially establishing … Read more
This paper has a two-fold focus on proving that the quasimetric and the weak $\tau$-distance versions of the Ekeland variational principle are equivalent in the sense that one implies the other and on presenting the need of such extensions for possible applications in the formation and break of workers hiring and firing routines. ArticleDownload View … Read more
In this paper we discuss the complexity of a dynamic spectrum management problem within a multi-user communication system with K users and N available tones. In this problem a common utility function is optimized. In particular, so called min-rate, harmonic mean and geometric mean utility functions are considered. The complexity of the optimization problems with … Read more
We consider the problem of minimizing a continuous function f over a compact set K. We analyze a hierarchy of upper bounds proposed by Lasserre in [SIAM J. Optim. 21(3) (2011), pp. 864-885], obtained by searching for an optimal probability density function h on K which is a sum of squares of polynomials, so that … Read more
In this paper we present a variant of the proximal forward-backward splitting method for solving nonsmooth optimization problems in Hilbert spaces, when the objective function is the sum of two nondifferentiable convex functions. The proposed iteration, which will be call the Proximal Subgradient Splitting Method, extends the classical projected subgradient iteration for important classes of … Read more
In this paper we consider an aggregation technique introduced by Yildiran, 2009 to study the convex hull of regions defined by two quadratic or by a conic quadratic and a quadratic inequality. Yildiran shows how to characterize the convex hull of open sets defined by two strict quadratic inequalities using Linear Matrix Inequalities (LMI). We … Read more
The rank minimization with linear equality constraints has two closely related models, the low rank approximation model, that is to find the best rank-k approximation of a matrix satisfying the linear constraints, and its corresponding factorization model. The latter one is an unconstrained nonlinear least squares problem and hence enjoys a few fast first-order methods … Read more