Linear complementarity, linear and nonlinear programming

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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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Journal Article•DOI•

Technical Note: Propagating correlations in atmospheric inversions using different Kalman update smoothers

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Jinyun Tang¹, Q. Zhuang¹•Institutions (1)

Purdue University¹

02 Feb 2011-Atmospheric Chemistry and Physics

TL;DR: In this paper, the fixed-lag ensemble square root Kalman smoother and fixed-latency square root sigma-point Kalman smoothing were proposed to propagate correlations between on-line and online state variables.

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Abstract: . The scheme to propagate correlations between on-line and off-line state variables in atmospheric inversions using the fixed-lag Kalman smoother proposed in Bruhwiler et al. (2005) is explained as a process to impose a balanced constraint on the on-line state variables. It is then extended to the fixed-lag ensemble square root Kalman smoother and fixed-lag square root sigma-point Kalman smoother, allowing us to treat nonlinear observation operators easily. Further, to constrain the posterior fluxes within their feasible ranges, the constrained fixed-lag Kalman smoother is presented and the variable transform technique is proposed for the other two smoothers. Comparisons between various methods and observational data are conducted using a synthetic inversion of atmospheric CH 4 fluxes. The results indicate that our developed methods are good alternatives to existing methods for conducting sequential inversion of atmospheric trace gases. It is also shown that the benefit to include the correlations between on-line and off-line state variables is case dependent.

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3 citations

Cites methods from "Linear complementarity, linear and ..."

...We use the method associated with the concept of active set (Murty, 1988) to solve the above optimization problem iteratively....
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...2.2, the following minimization problem is solved J2 = ( s++u −s + u )T (Q+uu)−1(s++u −s+u ) lbu ≤ s ++ u ≤ ubu (38) We use the method associated with the concept of active set (Murty, 1988) to solve the above optimization problem iteratively....
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Journal Article•DOI•

A mathematical programming incremental formulation for unilateral frictional contact problems of linear elasticity

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I. N. Doudoumis

01 Jun 2003-Applicable Analysis

TL;DR: In this paper, a detailed analytical formulation of the unilateral contact boundary conditions with Coulomb's law of dry friction is first attempted and the quasi-static contact problem between 3D elastic bodies is studied thereafter.

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Abstract: In this article a detailed analytical formulation of the unilateral contact boundary conditions with Coulomb's law of dry friction is first attempted and the quasi-static contact problem between 3-D elastic bodies is studied thereafter. Discretizing the bodies by the Finite Element Method, introducing fictitious contact bonds and using the concept of the equivalent structural system, an incremental Nonlinear Complementarity Problem is finally formulated. Then, using additional simplifying assumptions, this problem can be transformed into an incremental Linear Complementarity Problem.

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2 citations

Cites background or methods from "Linear complementarity, linear and ..."

...A substantial simplification of the NLCP may be done by its transformation to a LCP, whose the numerical solution can be performed by using certain computational algorithms [10] of direct (principal pivoting, Lemke’s etc....
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...Usually this problem can be transformed to a non-linear programming problem or to a fixed point computing problem [10]....
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Proceedings Article•DOI•

A New Approach for solving the Linear Complementarity Problem Using Smoothing Functions

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El Hassene Osmani¹, Mounir Haddou¹, Lina Abdallah²•Institutions (2)

University of Rennes¹, Lebanese University²

19 May 2021

TL;DR: Based on smoothing techniques, the authors proposed some new methods to solve linear complementarity problems, which avoided any parameter management while ensuring good theoretical convergence results. But the most severe difficulty that awaits us is the nondifferentiability of the complementarity conditions.

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Abstract: Based on smoothing techniques, we propose some new methods to solve linear complementarity problems (LCP). The idea of these new algorithms takes inspiration from interior point methods. The technique that we propose avoids any parameter management while ensuring good theoretical convergence results. These are validated by extensive numerical tests, in which we compare the new methods to several other classical methods. Our objective is to work out an efficient and robust numerical method to solve linear complementarity problems. The most severe difficulty that awaits us is the non-differentiability of the complementarity conditions.

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2 citations

Journal Article•DOI•

A Self-Adaptive Projection and Contraction Method for Linear Complementarity Problems

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Li-Zhi Liao¹, Shengli Wang¹•Institutions (1)

Hong Kong Baptist University¹

28 May 2003-Applied Mathematics and Optimization

TL;DR: In this article, a self-adaptive projection and contraction method for the linear complementarity problem (LCP) is proposed. But the method is not suitable for the case of the linear complearity problem with a fixed number of nodes.

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Abstract: In this paper we develop a self-adaptive projection and contraction method for the linear complementarity problem (LCP). This method improves the practical performance of the modified projection and contraction method in [10] by adopting a self-adaptive technique. The global convergence of our new method is proved under mild assumptions. Our numerical tests clearly demonstrate the necessity and effectiveness of our proposed method.

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2 citations

Book Chapter•DOI•

The Extended Linear Complementarity Problem and Its Applications in Analysis and Control of Discrete-Event Systems

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Bart De Schutter¹•Institutions (1)

Delft University of Technology¹

01 Jan 2008

TL;DR: This chapter gives an overview of complementarity problems with a special focus on the extended linear complementarity problem (ELCP) and its applications in analysis and control of discrete-event systems such as traffic signal controlled intersections, manufacturing systems, railway networks, etc.

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Abstract: In this chapter, we give an overview of complementarity problems with a special focus on the extended linear complementarity problem (ELCP) and its applications in analysis and control of discrete-event systems such as traffic signal controlled intersections, manufacturing systems, railway networks, etc. We start by giving an introduction to the (regular) linear complementarity problem (LCP). Next, we discuss some extensions, with a particular emphasis on the ELCP, which can be considered to be the most general linear extension of the LCP. We then discuss some algorithms to compute one or all solutions of an ELCP. Next, we present a link between the ELCP and max-plus equations. This is then the basis for some applications of the ELCP in analysis and model-based predictive control of a special class of discrete-event systems. We also show that — although the general ELCP is NP-hard — the ELCP-based control problem can be transformed into a linear programming problem, which can be solved in polynomial time.

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2 citations

Cites background or methods from "Linear complementarity, linear and ..."

...The Linear Complementarity Problem (LCP) is one of the fundamental problems in optimization and mathematical programming (Cottle et al., 1992; Murty, 1988)....
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...For more information on the generalizations discussed above and for applications and methods to solve these problems the interested reader may consult the references cited above and (Andreani and Martı́nez, 1998; Ebiefung and Kostreva, 1992; Isac, 1992; Júdice and Vicente, 1994; Mangasarian, 1995; McShane, 1994; Mohan et al., 1996; Murty, 1988; Vandenberghe et al., 1989; Zhang, 1994) and the references therein....
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...For algorithms to solve a (regular) LCP we refer to (Bai, 1999; Chen and Mangasarian, 1995; Cottle et al., 1992; Kaliski and Ye, 1993; Kanzow, 1996; Kočvara and Zowe, 1994; Kremers and Talman, 1994; Mehrotra and Stubbs, 1994; Murty, 1988; Pardalos and Resende, 2002; Schäfer, 2004; Sheng and Potra, 1997; Wright, 1994; Yuan and Song, 2003) and the references therein....
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...…the interested reader may consult the references cited above and (Andreani and Martı́nez, 1998; Ebiefung and Kostreva, 1992; Isac, 1992; Júdice and Vicente, 1994; Mangasarian, 1995; McShane, 1994; Mohan et al., 1996; Murty, 1988; Vandenberghe et al., 1989; Zhang, 1994) and the references therein....
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...…Mangasarian, 1995; Cottle et al., 1992; Kaliski and Ye, 1993; Kanzow, 1996; Kočvara and Zowe, 1994; Kremers and Talman, 1994; Mehrotra and Stubbs, 1994; Murty, 1988; Pardalos and Resende, 2002; Schäfer, 2004; Sheng and Potra, 1997; Wright, 1994; Yuan and Song, 2003) and the references therein....
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Linear complementarity, linear and nonlinear programming

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Cites methods from "Linear complementarity, linear and ..."

Cites background or methods from "Linear complementarity, linear and ..."

Cites background or methods from "Linear complementarity, linear and ..."

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