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Linear complementarity, linear and nonlinear programming
01 Jan 1988-
About: The article was published on 1988-01-01 and is currently open access. It has received 1012 citations till now. The article focuses on the topics: Mixed complementarity problem & Complementarity theory.
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TL;DR: In this article, a convex, multilevel decomposition approach is proposed for the solution of static analysis problems involving non-monotone, possibly multivalued laws.
10 citations
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TL;DR: It is proved that WNNM can be equivalently transformed into a quadratic programming problem with linear constraints and its global optimum can be readily achieved by off-the-shelf convex optimization solvers.
Abstract: In recent years, the nuclear norm minimization (NNM) problem has been attracting much attention in computer vision and machine learning. The NNM problem is capitalized on its convexity and it can be solved efficiently. The standard nuclear norm regularizes all singular values equally, which is however not flexible enough to fit real scenarios. Weighted nuclear norm minimization (WNNM) is a natural extension and generalization of NNM. By assigning properly different weights to different singular values, WNNM can lead to state-of-the-art results in applications such as image denoising. Nevertheless, so far the global optimal solution of WNNM problem is not completely solved yet due to its non-convexity in general cases. In this article, we study the theoretical properties of WNNM and prove that WNNM can be equivalently transformed into a quadratic programming problem with linear constraints. This implies that WNNM is equivalent to a convex problem and its global optimum can be readily achieved by off-the-shelf convex optimization solvers. We further show that when the weights are non-descending, the globally optimal solution of WNNM can be obtained in closed-form.
10 citations
TL;DR: In this article, the semi-smooth Newton method was applied to the convex quadratic programming problem under positive constraints. And the results showed that the generated sequence is bounded, for any starting point, and a formula for any accumulation point of this sequence is presented.
10 citations
TL;DR: In this article, a collision-driven discrete particle simulation framework is presented for investigating the dynamics of a jet of erosive particles impacting a surface with a specified porosity and compliance.
Abstract: The general problem of a loosely flowing erosive granular jet undergoing impact with a compliant surface is common in many manufacturing processes, and also in the operating environment of a variety of machine parts. This paper presents a three-dimensional, collision-driven discrete particle simulation framework for investigating the dynamics of a jet of erosive particles impacting a surface with a specified porosity and compliance. The framework is capable of handling repeated collisions between incoming particles and rebounding particles, and between particles and surfaces. It is also capable of performing a coupled simultaneous calculation of sub-surface stresses in the material, assuming a certain porosity. Well illustrated numerical examples are presented with detailed analysis for investigations on the mechanics and energetics of the interfering collisions in eroding jets close to the target surface, on the effect of such interference on the material erosion, and on the evolving stress levels and potential damage zones under the action of impact. Particularly, the assumption of considering first-order collisions between oncoming and rebounding jet particles is re-examined. The influence of repeated collisions on energy transferred to the surface was found to be significant under conditions which involves high particle numbers or fluxes, and also high degrees of inelasticity. The overall trends for parametric variations were found to be in accordance with reported trends in the literature.
10 citations
Cites background from "Linear complementarity, linear and ..."
...The latest developments, as discussed in the review, incorporate the idea of impulsive forces in rigid body dynamics, as measures of distributions instead, and the idea of combining rigid body contact problems with an area of convex analysis called the linear complementarity problem (for mathematical foundations of the method see the text by Murty [36])....
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TL;DR: In this paper, it was shown that property (∗ ∗) is also sufficient for a Lipschitzian matrix to be in Q 0, and that if A has this property, then A and all its PPTs must be completely Q 0 ; further, for any q, the linear complementarity problem ( q, A ) can be processed by a simple principal pivoting method.
10 citations