نتایج جستجو برای: primal strong co

تعداد نتایج: 696981  

Journal: :Numerische Mathematik 2000
Weimin Han B. Daya Reddy

This work considers semi-and fully discrete approximations to the primal problem in elastoplas-ticity. The unknowns are displacement and internal variables, and the problem takes the form of an evolution variational inequality. Strong convergence of time-discrete, as well as spatially and fully discrete approximations, is established without making any assumptions of regularity over and above t...

Journal: :Math. Meth. of OR 2007
Gert Wanka Radu Ioan Bot Emese Vargyas

For an optimization problem with a composed objective function and composed constraint functions we determine, by means of the conjugacy approach based on the perturbation theory, some dual problems to it. The relations between the optimal objective values of these duals are studied. Moreover sufficient conditions are given in order to achieve equality between the optimal objective values of th...

2010
Radu Ioan Boţ Sorin-Mihai Grad

Considering a vector optimization problem to which properly efficient solutions are defined by using convex cone-monotone scalarization functions, we attach to it, by means of perturbation theory, new vector duals. When the primal problem, the scalarization function and the perturbation function are particularized, different dual vector problems are obtained, some of them already known in the l...

2006
Alexander Kruger

The paper investigates stationarity and regularity concepts for set systems in a normed space. Several primal and dual constants characterizing these properties are introduced and the relations between the constants are established. The equivalence between the regularity property and the strong metric inequality is established. The extended extremal principle is formulated. keywords: nonsmooth ...

Journal: :J. Optimization Theory and Applications 2011
Lingchen Kong Levent Tunçel Naihua Xiu

In this paper we consider the linear symmetric cone programming (SCP). At a KarushKuhn-Tucker (KKT) point of SCP, we present the important equivalent conditions for the nonsingularity of Clarke’s generalized Jacobian of the KKT nonsmooth system, such as primal and dual constraint nondegeneracy, the strong regularity, and the nonsingularity of the B-subdifferential of the KKT system. This affirm...

2014
Mingyi Hong Tsung-Hui Chang Xiangfeng Wang Meisam Razaviyayn Shiqian Ma Zhi-Quan Luo

Consider the problem of minimizing the sum of a smooth convex function and a separable nonsmooth convex function subject to linear coupling constraints. Problems of this form arise in many contemporary applications including signal processing, wireless networking and smart grid provisioning. Motivated by the huge size of these applications, we propose a new class of first order primal-dual algo...

2007
Angelia Nedić Asuman Ozdaglar

We study primal solutions obtained as a by-product of subgradient methods when solving the Lagrangian dual of a primal convex constrained optimization problem (possibly nonsmooth). The existing literature on the use of subgradient methods for generating primal optimal solutions is limited to the methods producing such solutions only asymptotically (i.e., in the limit as the number of subgradien...

2007
Jos F. Sturm Shuzhong Zhang

In this paper we introduce a primal-dual affine scaling method. The method uses a searchdirection obtained by minimizing the duality gap over a linearly transformed conic section. This direction neither coincides with known primal-dual affine scaling directions [12, 21], nor does it fit in the generic primal-dual method [15]. The new method requires O(√nL) main iterations. It is shown that the ...

Journal: :Math. Program. 2018
Patrick L. Combettes Jonathan Eckstein

We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the sense that, at each iteration, only a subset of the monotone operators needs to be processed, as opposed to all operators as in established methods. Determinist...

2015
Patrick L. Combettes Jonathan Eckstein

We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the sense that, at each iteration, only a subset of the monotone operators needs to be processed, as opposed to all operators as in established methods. Determinist...

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