In this paper, we study the semilocal convergence on a class of improved Chebyshev methods for solving nonlinear equations in Banach spaces. Different from the results for Chebyshev method considered in Hernández and Salanova (J Comput Appl Math 126:131–143, <CitationRef CitationID="CR5">2000</CitationRef>), these methods are free from...</citationref>

<Para ID="Par1">Recently, a walk-and-round heuristic was proposed by Huang and Mehrotra (Comput Optim Appl, <CitationRef CitationID="CR24">2012</CitationRef>) for generating high quality feasible solutions of mixed integer linear programs. This approach uses geometric random walks on a polyhedral set to sample points in this set. It subsequently rounds...</citationref></para>

<Para ID="Par1">Sometimes, the feasible set of an optimization problem that one aims to solve using a Nonlinear Programming algorithm is empty. In this case, two characteristics of the algorithm are desirable. On the one hand, the algorithm should converge to a minimizer of some infeasibility measure. On the...</para>

<Para ID="Par1">We consider a class of nonsmooth convex optimization problems where the objective function is a convex differentiable function regularized by the sum of the group reproducing kernel norm and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\ell _1$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>ℓ</mi> <mn>1</mn> </msub> </math> </EquationSource> </InlineEquation>-norm of the problem variables. This class of problems has many applications in...</equationsource></equationsource></inlineequation></para>

<Para ID="Par1">The mesh adaptive direct search (<Emphasis Type="SmallCaps">Mads) algorithm is designed for blackbox optimization problems subject to general inequality constraints. Currently, <Emphasis Type="SmallCaps">Mads does not support equalities, neither in theory nor in practice. The present work proposes extensions to treat problems with linear equalities...</emphasis></emphasis></para>

<Para ID="Par1">We describe the most recent evolution of our constrained and unconstrained testing environment and its accompanying SIF decoder. Code-named <Emphasis FontCategory="SansSerif">SIFDecode and <Emphasis FontCategory="SansSerif">CUTEst, these updated versions feature dynamic memory allocation, a modern thread-safe Fortran modular design, a new Matlab interface and a...</emphasis></emphasis></para>

In this paper, we combine two types of local search algorithms for global optimization of continuous functions. In the literature, most of the hybrid algorithms are produced by combination of a global optimization algorithm with a local search algorithm and the local search is used to improve...

This paper presents a decomposition strategy applicable to DAE constrained optimization problems. A common solution method for such problems is to apply a direct transcription method and solve the resulting nonlinear program using an interior-point algorithm. For this approach, the time to solve...

In this work we analyze a first order method especially tailored for smooth saddle point problems, based on an alternating extragradient scheme. The proposed method is based on three successive projection steps, which can be computed also with respect to non Euclidean metrics. The stepsize...