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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 ArticleDOI
TL;DR: In this paper, the orthogonal projection of the current point onto a hyperplane corresponds to a surrogate constraint which is constructed through a positive combination of a group of violated constraints.
Abstract: New iterative methods for solving systems of linear inequalities are presented Each step in these methods consists of finding the orthogonal projection of the current point onto a hyperplane corresponding to a surrogate constraint which is constructed through a positive combination of a group of violated constraints Both sequential and parallel implementations are discussed

65 citations

01 Jan 2006
TL;DR: These annotated slides were prepared by Jeff Fessler for attendees of the ISBI tutorial on statistical image reconstruction methods to provide supplemental details, and particularly to provide extensive literature references for further study.
Abstract: 0.0 c © J. Fessler, March 15, 2006 p0intro These annotated slides were prepared by Jeff Fessler for attendees of the ISBI tutorial on statistical image reconstruction methods. The purpose of the annotation is to provide supplemental details, and particularly to provide extensive literature references for further study. For a fascinating history of tomography, see [1]. For broad coverage of image science, see [2]. For further references on image reconstruction, see review papers and chapters, e.g., [3–9].

65 citations

Journal ArticleDOI
TL;DR: In this paper, Farkas' Lemma in combination with bilevel programming and disjoint bilinear programming can be used to search for problematic initial states which lack recursive feasibility, thus invalidating a particular MPC controller.

64 citations

Book ChapterDOI
01 Oct 2009
TL;DR: A new modeling method for the insertion of needles and more generally thin and flexible medical devices into soft tissues is presented, which allows for the 3D simulation of different physical phenomena such as puncture, cutting, static and dynamic friction at interactive frame rate.
Abstract: This paper presents a new modeling method for the insertion of needles and more generally thin and flexible medical devices into soft tissues. Several medical procedures rely on the insertion of slender medical devices such as biopsy, brachytherapy, deep-brain stimulation. In this paper, the interactions between soft tissues and flexible instruments are reproduced using a set of dedicated complementarity constraints. Each constraint is positionned and applied to the deformable models without requiring any remeshing. Our method allows for the 3D simulation of different physical phenomena such as puncture, cutting, static and dynamic friction at interactive frame rate. To obtain realistic simulation, the model can be parametrized using experimental data. Our method is validated through a series of typical simulation examples and new more complex scenarios.

63 citations

Journal ArticleDOI
TL;DR: This work argues that, in a map showing a network of roads relevant to the user, distortion should preferably take place in those areas where the network is sparse, and compute a new spatial mapping with a graph-based optimization approach, minimizing the square sum of distortions at edges.
Abstract: Mobile users of maps typically need detailed information about their surroundings plus some context information about remote places. In order to avoid that the map partly gets too dense, cartographers have designed mapping functions that enlarge a user-defined focus region - such functions are sometimes called fish-eye projections. The extra map space occupied by the enlarged focus region is compensated by distorting other parts of the map. We argue that, in a map showing a network of roads relevant to the user, distortion should preferably take place in those areas where the network is sparse. Therefore, we do not apply a predefined mapping function. Instead, we consider the road network as a graph whose edges are the road segments. We compute a new spatial mapping with a graph-based optimization approach, minimizing the square sum of distortions at edges. Our optimization method is based on a convex quadratic program (CQP); CQPs can be solved in polynomial time. Important requirements on the output map are expressed as linear inequalities. In particular, we show how to forbid edge crossings. We have implemented our method in a prototype tool. For instances of different sizes, our method generated output maps that were far less distorted than those generated with a predefined fish-eye projection. Future work is needed to automate the selection of roads relevant to the user. Furthermore, we aim at fast heuristics for application in real-time systems.

62 citations


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

  • ...If the objective function is convex, however, the problem can be solved ef ciently [23]....

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