Book•
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.
Citations
More filters
Posted Content•
TL;DR: In this paper, a super-hedging strategy for the variance swap is proposed, based on the results of Rost and Chacon, and a proof of optimality of the upper bound is provided.
Abstract: Robust, or model-independent properties of the variance swap are well-known, and date back to Dupire and Neuberger, who showed that, given the price of co-terminal call options, the price of a variance swap was exactly specified under the assumption that the price process is continuous. In Cox and Wang we showed that a lower bound on the price of a variance call could be established using a solution to the Skorokhod embedding problem due to Root. In this paper, we provide a construction, and a proof of optimality of the upper bound, using results of Rost and Chacon, and show how this proof can be used to determine a super-hedging strategy which is model-independent. In addition, we outline how the hedging strategy may be computed numerically. Using these methods, we also show that the Heston-Nandi model is 'asymptotically extreme' in the sense that, for large maturities, the Heston-Nandi model gives prices for variance call options which are approximately the lowest values consistent with the same call price data.
19 citations
Cites methods from "Linear complementarity, linear and ..."
...We refer to Murty [36] for details on the numerical implementation of the Complementary Pivot algorithm....
[...]
TL;DR: A fast numerical solver for a nonlinear constrained optimization problem, arising from 3D concentrated frictional shift and rolling contact problems with dry Coulomb friction, with a significant reduction of the computational time compared to existing solvers for concentrated contact problems.
19 citations
Cites methods from "Linear complementarity, linear and ..."
...It applies an active set strategy [24], which leads to systems of nonlinear equations that are solved using Newton’s method and Gauss-elimination (GE)....
[...]
TL;DR: It is shown that this closedness condition is satisfied by the class of polyhedral multifunctions, which seems to be new in the context of existence proof for the multivalued complementarity problem.
Abstract: This paper presents some new results for the existence of a solution to a multivalued complementary problem. These results are derived under a "upper limiting homogeneity" ULH property on the multifunction defining the complementarity problem and on a certain closedness/interiority condition. The closedness condition seems to be new in the context of existence proof for the multivalued complementarity problem. We show that this closedness condition is satisfied by the class of polyhedral multifunctions.
19 citations
TL;DR: In this paper, a weaker version of the class of generalized positive subdefinite matrices introduced by Crouzeix and Komlosi is presented, which is new in the literature, and obtain some properties of weak generalized PSBD matrices.
Abstract: In this article, we present a weaker version of the class of generalized positive subdefinite matrices introduced by Crouzeix and Komlosi [J.P. Crouzeix and S. Komlosi, The Linear Complementarity Problem and the Class of Generalized Positive Subdefinite Matrices, Applied Optimization, Vol. 59, Kluwer, Dordrecht, 2001, pp. 45–63], which is new in the literature, and obtain some properties of weak generalized positive subdefinite (WGPSBD) matrices. We show that this weaker class of matrices is also captured by row-sufficient matrices introduced by Cottle et al. [R.W. Cottle, J.S. Pang, and V. Venkateswaran, Sufficient matrices and the linear complementarity problem, Linear Algebra Appl. 114/115 (1989), pp. 231–249] and show that for WGPSBD matrices under appropriate assumptions, the solution set of a linear complementarity problem is the same as the set of Karush–Kuhn–Tucker-stationary points of the corresponding quadratic programming problem. This further extends the results obtained in an earlier paper by...
19 citations
Book•
01 Jun 1995
TL;DR: The topics covered include object-oriented constraint programming, object- oriented modeling of graphics applications to handle complexity,object-oriented techniques for developing user interfaces, and 3D modeling and rendering.
Abstract: From the Publisher:
Object-oriented concepts are particularly applicable to computer graphics in its broadest sense, including interaction, image synthesis, animation, and computer aided design. The use of object-oriented techniques in computer graphics is a widely acknowledged way of dealing with the complexities encountered in graphics systems. But the field of object-oriented graphics (OOG) is still young and full of problems. This book reports on latest advances in this field and discusses how the discipline of OOG is being explored and developed. The topics covered include object-oriented constraint programming, object-oriented modeling of graphics applications to handle complexity, object-oriented techniques for developing user interfaces, and 3D modeling and rendering.
19 citations