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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 paper, a quasi-feed-in-tariff (QFIT) policy formulation is presented for micro-grids that integrates renewable energy generation considering policy makers and GENCOs objectives assuming a bi-level multi-period formulation.
23 citations
Cites background from "Linear complementarity, linear and ..."
...Complementarity problems find the problem solution, as well as the optimization problem's multipliers (Murty and Yu, 1997)....
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...Murty and Yu (1997), Duan et al. (2010), and Gabriel et al. (2012) provide various algorithms that are used to solve both LCPs and NCPs....
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TL;DR: In this article, the generalized eigenvalue complementarity problem for tensors (GEiCPT) is addressed, which arises from the stability analysis of finite dimensional mechanical systems and find applications in differential dynamical systems.
Abstract: In this paper, the generalized eigenvalue complementarity problem for tensors (GEiCPT) is addressed, which arises from the stability analysis of finite dimensional mechanical systems and find applications in differential dynamical systems. The general properties of the (GEiCP-T) have been studied. We establish its relationship with the generalized tensor eigenvalue problem. It follows that if exist, the number of �-solutions can be bounded. We also give some sufficient conditions for the existence of the solution. In particular, there exists a unique solution of the (EiCP-T) (i.e., J = [n]) for irreducible nonnegative tensors. For the symmetric case, we derive a sufficient and necessary condition for the solvability of the (GEiCP-T) by reformulating it as a nonlinear program. It has also been proved that deciding the solvability of the (EiCP-T) is NP-hard in general. Moreover, a shifted projected power method is proposed to solve the symmetric (GEiCP-T). The monotonic convergence is also established. The numerical experiments demonstrate convergence behavior of our method and show that the algorithm presented is promising.
22 citations
TL;DR: A two-dimensional displacement discontinuity method in combination with a complementarity solver to simulate quasi-static slip on cracks as models for faults and fractures in an otherwise homogeneous, isotropic, linear elastic material.
22 citations
TL;DR: In this paper, different numerical methods for a two-phase free boundary problem are discussed and an efficient algorithm based on the finite element method is presented, which converges to the solution of the given free boundary problems.
22 citations
TL;DR: A model describing the dynamics of a population of ice floes with arbitrary shapes and sizes, which are exposed to atmospheric and oceanic skin drag is presented, and it is suggested that collisional regimes of floe dispersion at small scales are different from a large-scale regime essentially driven by wind forcing.
Abstract: In this paper, we present a model describing the dynamics of a population of ice floes with arbitrary shapes and sizes, which are exposed to atmospheric and oceanic skin drag. The granular model presented is based on simplified momentum equations for ice floe motion between collisions and on the resolution of linear complementarity problems to deal with ice floe collisions. Between collisions, the motion of an individual ice floe satisfies the linear and angular momentum conservation equations, with classical formula applied to account for atmospheric and oceanic skin drag. To deal with collisions, before they lead to interpenetration, we included a linear complementarity problem based on the Signorini condition and Coulombs law. The nature of the contact is described through a constant coefficient of friction μ, as well as a coefficient of restitution (0≤e≤1) describing the loss of kinetic energy during the collision. In the present version of our model, this coefficient is fixed. The model was validated using data obtained from the motion of interacting artificial wood floes in a test basin. The results of simulations comprising few hundreds of ice floes of various shapes and sizes, exposed to different forcing scenarios, and under different configurations, are also discussed. They show that the progressive clustering of ice floes as the result of kinetic energy dissipation during collisions is well captured, and suggest a collisional regimes of floe dispersion at small scales, different from a large-scale regime essentially driven by wind forcing.
22 citations