For solving non-smooth multidimensional optimization problems, we present a family of relaxation subgradient methods (RSMs) with built-in algorithm for finding the descent direction that forms an acute angle all subgradients in neighborhood current minimum. Minimizing function along opposite (with minus sign) enables to go beyond The algorithms is based on systems inequalities. finite convergen...

Abstract We present natural-age-grid Galerkin methods for a model of a biological population undergoing aging. We use a mollified birth term in the method and analysis. The error due to mollification is of arbitrary order, depending on the choice of mollifier. The methods in this paper generalize the methods presented in [1], where the approximation space in age was taken to be a discontinuous ...

We introduce an intrinsic notion of Zygmund regularity for Colombeau algebras of generalized functions. In case of embedded distributions belonging to some Zygmund-Hölder space this is shown to be consistent. The definition is motivated by the well-known use of the wavelet transform as a tool in studying Hölder regularity. It is based on a simple mollifier-wavelet interplay which translates wav...

The contribution deals with timestepping schemes for nonsmooth dynamical systems. Traditionally, these schemes are locally of integration order one, both in smooth and nonsmooth periods. This is inefficient for applications with few events like circuit breakers, valve trains or slider-crank mechanisms. To improve the behavior during smooth episodes, we start activities twofold. First, we includ...

In this work, we introduce a variant of the standard mollifier technique that is valid up to the boundary of a Lipschitz domain in Rn. A version of Friedrichs’s lemma is derived that gives an estimate up to the boundary for the commutator of the multiplication by a Lipschitz function and the modified mollification. We use this version of Friedrichs’s lemma to prove the density of smooth functio...

recently, gasimov and yenilmez proposed an approach for solving two kinds of fuzzy linear programming (flp) problems. through the approach, each flp problem is first defuzzified into an equivalent crisp problem which is non-linear and even non-convex. then, the crisp problem is solved by the use of the modified subgradient method. in this paper we will have another look at the earlier defuzzifi...

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 iterations, which total cost depends logarithmically in the dimension. This technique is based on a recu...

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 iterations, which total cost depends logarithmically in the dimension. This technique is based on a recu...

We report on the implementation and computational testing of several versions of a set covering algorithm, based on the family of cutting planes from conditional bounds discussed in the companion paper [2]. The algorithm uses a set of heuristics to find prime covers, another set of heuristics to find feasible solutions to the dual linear program which are needed to generate cuts, and subgradien...