The quadratically convergent algorithms for training SVM with smoothing methods are discussed in this paper. By smoothing the objective function of an SVM formulation, Lee and Mangasarian [Comput. Optim. Appl. 20(1):5-22, <CitationRef CitationID="CR17">2001</CitationRef>] presented one such algorithm called SSVM and proved that the error...</citationref>

In this paper, we propose a Shamanskii-like Levenberg-Marquardt method for nonlinear equations. At every iteration, not only a LM step but also m−1 approximate LM steps are computed, where m is a positive integer. Under the local error bound condition which is weaker than nonsingularity, we...

We introduce a class of adaptive non-smooth convex variational problems for image denoising in terms of a common data fitting term and a support functional as regularizer. Adaptivity is modeled by a set-valued mapping with closed, compact and convex values, that defines and steers the...

We present a second order image decomposition model to perform denoising and texture extraction. We look for the decomposition f=u+v+w where u is a first order term, v a second order term and w the (0 order) remainder term. For highly textured images the model gives a two-scale texture...

In recent years, convex optimization methods were successfully applied for various image processing tasks and a large number of first-order methods were designed to minimize the corresponding functionals. Interestingly, it was shown recently in Grewenig et al. (<CitationRef CitationID="CR24">2010</CitationRef>) that the simple idea of...</citationref>

Two trust regions algorithms for unconstrained nonlinear optimization problems are presented: a monotone and a nonmonotone one. Both of them solve the trust region subproblem by the spectral projected gradient (SPG) method proposed by Birgin, Martínez and Raydan (in SIAM J. Optim....

This paper presents several methodological and algorithmic improvements over a state-of-the-art dynamic programming algorithm for solving the bi-objective {0,1} knapsack problem. The variants proposed make use of new definitions of lower and upper bounds, which allow a large number of states to...

This paper introduces a second-order differentiability smoothing technique to the classical l <Subscript>1</Subscript> exact penalty function for constrained optimization problems(COP). Error estimations among the optimal objective values of the nonsmooth penalty problem, the smoothed penalty problem and the original...</subscript>

This paper presents a novel formulation of Multi Agent Collaborative Search, for multi-objective optimization, based on Tchebycheff decomposition. A population of agents combines heuristics that aim at exploring the search space both globally (social moves) and in a neighborhood of each agent...

Given a simple undirected graph, the problem of finding a maximum subset of vertices satisfying a nontrivial, interesting property Π that is hereditary on induced subgraphs, is known to be NP-hard. Many well-known graph properties meet the above conditions, making the problem widely applicable....