A new decomposition optimization algorithm, called path-following gradient-based decomposition, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this algorithm does not require any smoothness assumption on the...

<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>

In this paper, we suggest an algorithm for price adjustment towards a partial market equilibrium. Its convergence properties are crucially based on Convex Analysis. Our price adjustment corresponds to a subgradient scheme for minimizing a special nonsmooth convex function. This function is the...

We consider a class of nonsmooth convex optimization problems where the objective function is the composition of a strongly convex differentiable function with a linear mapping, regularized by the group reproducing kernel norm. This class of problems arise naturally from applications in group...

We consider a new class of huge-scale problems, the problems with sparse subgradients. The most important functions of this type are piece-wise linear. For optimization problems with uniform sparsity of corresponding linear operators, we suggest a very efficient implementation of subgradient...

In this paper we propose and analyze a variant of the level method [4], which is an algorithm for minimizing nonsmooth convex functions. The main work per iteration is spent on 1) minimizing a piecewise-linear model of the objective function and on 2) projecting onto the intersection of the...

Приводится система уравнений и неравенств, описывающая потокораспределение в трубопроводных системах с автоматическими регуляторами расхода на некоторых...

In this paper, we propose interior-point algorithms for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$P_* (\kappa )$$</EquationSource> </InlineEquation>-linear complementarity problem based on a new class of kernel functions. New search directions and proximity measures are defined based on these functions. We show that if a strictly feasible starting point is available,...</equationsource></inlineequation>