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Métodos duales y algoritmos híbridos para problemas de "set partitioning".

Jaime Barceló Bugeda, Elena Fernández Areizaga (1990)

Trabajos de Investigación Operativa

En este artículo estudiamos la utilización de métodos duales en el diseño de algoritmos híbridos para la resolución de problemas de "Set Partitioning" (SP). Las técnicas duales resultan de gran interés para resolver problemas con estructura combinatoria no sólo porque generan cotas inferiores sino porque, además, su utilización junto con heurísticas y procedimientos de generación de desigualdades en el diseño de algoritmos híbridos permite evaluar la calidad de las cotas superiores obtenidas. Los...

Minimización global de un polinomio en la recta real.

César Beltrán Royo (1999)

Qüestiió

En este artículo presentamos y probamos numéricamente un nuevo algoritmo para la minimización global de un polinomio de grado par. El algoritmo está basado en la simple idea de trasladar verticalmente el grafo del polinomio hasta que el eje OX sea tangente al grafo del polinomio trasladado. En esta privilegiada posición, cualquier raíz real del polinomio trasladado es un mínimo global del polinomio original.

Minimization of a convex quadratic function subject to separable conical constraints in granular dynamics

Pospíšil, Lukáš, Dostál, Zdeněk (2015)

Programs and Algorithms of Numerical Mathematics

The numerical solution of granular dynamics problems with Coulomb friction leads to the problem of minimizing a convex quadratic function with semidefinite Hessian subject to a separable conical constraints. In this paper, we are interested in the numerical solution of this problem. We suggest a modification of an active-set optimal quadratic programming algorithm. The number of projection steps is decreased by using a projected Barzilai-Borwein method. In the numerical experiment, we compare our...

Modifications of the limited-memory BFGS method based on the idea of conjugate directions

Vlček, Jan, Lukšan, Ladislav (2013)

Programs and Algorithms of Numerical Mathematics

Simple modifications of the limited-memory BFGS method (L-BFGS) for large scale unconstrained optimization are considered, which consist in corrections of the used difference vectors (derived from the idea of conjugate directions), utilizing information from the preceding iteration. For quadratic objective functions, the improvement of convergence is the best one in some sense and all stored difference vectors are conjugate for unit stepsizes. The algorithm is globally convergent for convex sufficiently...

New hybrid conjugate gradient method for nonlinear optimization with application to image restoration problems

Youcef Elhamam Hemici, Samia Khelladi, Djamel Benterki (2024)

Kybernetika

The conjugate gradient method is one of the most effective algorithm for unconstrained nonlinear optimization problems. This is due to the fact that it does not need a lot of storage memory and its simple structure properties, which motivate us to propose a new hybrid conjugate gradient method through a convex combination of β k R M I L and β k H S . We compute the convex parameter θ k using the Newton direction. Global convergence is established through the strong Wolfe conditions. Numerical experiments show the...

Nonlinear conjugate gradient methods

Lukšan, Ladislav, Vlček, Jan (2015)

Programs and Algorithms of Numerical Mathematics

Modifications of nonlinear conjugate gradient method are described and tested.

Nonlinear Rescaling Method and Self-concordant Functions

Richard Andrášik (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Nonlinear rescaling is a tool for solving large-scale nonlinear programming problems. The primal-dual nonlinear rescaling method was used to solve two quadratic programming problems with quadratic constraints. Based on the performance of primal-dual nonlinear rescaling method on testing problems, the conclusions about setting up the parameters are made. Next, the connection between nonlinear rescaling methods and self-concordant functions is discussed and modified logarithmic barrier function is...

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