Publication

Multiparametric Linear Complementarity Problems

Colin Neil Jones
2006
Conference Papers

Résumé

The linear complementarity problem (LCP) is a general problem that unifies linear and quadratic programs and bimatrix games. In this paper, we present an efficient algorithm for the solution to multiparametric linear complementarity problems (pLCPs) that are defined by positive semi-definite matrices. This class of problems includes the multiparametric linear (pLP) and semi-definite quadratic programs (pQP), where parameters are allowed to appear linearly in the cost and the right hand side of the constraints. We demonstrate that the proposed algorithm is equal in efficiency to the best of current pLP and pQP solvers for all problems that they can solve, and yet extends to a much larger class

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https://infoscience.epfl.ch/entities/publication/a27082f6-eeba-4f0b-886f-5840aeed4208

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Colin Neil Jones
2006
Conference Papers

Résumé

Source officielle

https://infoscience.epfl.ch/entities/publication/a27082f6-eeba-4f0b-886f-5840aeed4208

À propos de ce résultat

Concepts associés (18)

Definite matrix

In mathematics, a symmetric matrix with real entries is positive-definite if the real number is positive for every nonzero real column vector where is the transpose of . More generally, a Hermitian matrix (that is, a complex matrix equal to its conjugate transpose) is positive-definite if the real number is positive for every nonzero complex column vector where denotes the conjugate transpose of Positive semi-definite matrices are defined similarly, except that the scalars and are required to be positive or zero (that is, nonnegative).

Algorithme de Shor

En arithmétique modulaire et en informatique quantique, l’algorithme de Shor est un algorithme quantique conçu par Peter Shor en 1994, qui factorise un entier naturel N en temps O et en espace . Beaucoup de cryptosystèmes à clé publique, tels que le RSA, deviendraient vulnérables si l'algorithme de Shor était un jour implanté dans un calculateur quantique pratique. Un message chiffré avec RSA peut être déchiffré par factorisation de sa clé publique N, qui est le produit de deux nombres premiers.

Definite quadratic form

In mathematics, a definite quadratic form is a quadratic form over some real vector space V that has the same sign (always positive or always negative) for every non-zero vector of V. According to that sign, the quadratic form is called positive-definite or negative-definite. A semidefinite (or semi-definite) quadratic form is defined in much the same way, except that "always positive" and "always negative" are replaced by "never negative" and "never positive", respectively.

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