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Mathematical programming via the least-squares method

Evald Übi (2010)

Open Mathematics

The least-squares method is used to obtain a stable algorithm for a system of linear inequalities as well as linear and nonlinear programming. For these problems the solution with minimal norm for a system of linear inequalities is found by solving the non-negative least-squares (NNLS) problem. Approximate and exact solutions of these problems are discussed. Attention is mainly paid to finding the initial solution to an LP problem. For this purpose an NNLS problem is formulated, enabling finding...

Metasearch information fusion using linear programming

Gholam R. Amin, Ali Emrouznejad, Hamid Sadeghi (2012)

RAIRO - Operations Research - Recherche Opérationnelle

For a specific query merging the returned results from multiple search engines, in the form of a metasearch aggregation, can provide significant improvement in the quality of relevant documents. This paper suggests a minimax linear programming (LP) formulation for fusion of multiple search engines results. The paper proposes a weighting method to include the importance weights of the underlying search engines. This is a two-phase approach which in the first phase a new method for computing the importance...

Metasearch information fusion using linear programming

Gholam R. Amin, Ali Emrouznejad, Hamid Sadeghi (2012)

RAIRO - Operations Research

For a specific query merging the returned results from multiple search engines, in the form of a metasearch aggregation, can provide significant improvement in the quality of relevant documents. This paper suggests a minimax linear programming (LP) formulation for fusion of multiple search engines results. The paper proposes a weighting method to include the importance weights of the underlying search engines. This is a two-phase approach which in...

Minimizing and maximizing a linear objective function under a fuzzy max - * relational equation and an inequality constraint

Zofia Matusiewicz (2022)

Kybernetika

This paper provides an extension of results connected with the problem of the optimization of a linear objective function subject to max - * fuzzy relational equations and an inequality constraint, where * is an operation. This research is important because the knowledge and the algorithms presented in the paper can be used in various optimization processes. Previous articles describe an important problem of minimizing a linear objective function under a fuzzy max - * relational equation and an inequality constraint,...

Mixed complementarity problems for robust optimization equilibrium in bimatrix game

Guimei Luo (2012)

Applications of Mathematics

In this paper, we investigate the bimatrix game using the robust optimization approach, in which each player may neither exactly estimate his opponent’s strategies nor evaluate his own cost matrix accurately while he may estimate a bounded uncertain set. We obtain computationally tractable robust formulations which turn to be linear programming problems and then solving a robust optimization equilibrium can be converted to solving a mixed complementarity problem under the l 1 ∩ l ∞ -norm. Some numerical...

Modelos auxiliares para problemas de programación lineal con coeficientes imprecisos en las restricciones.

Luis M. de Campos Ibáñez, José Luis Verdegay (1989)

Trabajos de Investigación Operativa

En este artículo se considera un programa de Programación Lineal en el que los coeficientes del sistema de inecuaciones lineales, que definen el conjunto de restricciones, están dados de forma imprecisa o vaga. Se supone entonces que tales coeficientes pueden ser definidos mediante números difusos. Se propone un enfoque de resolución basado en las distintas versiones existentes para la comparación de números difusos. Finalmente, se obtienen diferentes modelos auxiliares de Programación Lineal, que...

Multiobjective De Novo Linear Programming

Petr Fiala (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Mathematical programming under multiple objectives has emerged as a powerful tool to assist in the process of searching for decisions which best satisfy a multitude of conflicting objectives. In multiobjective linear programming problems it is usually impossible to optimize all objectives in a given system. Trade-offs are properties of inadequately designed system a thus can be eliminated through designing better one. Multiobjective De Novo linear programming is problem for designing optimal system...

Multiparametric linear fractional functionals programming.

Shyam S. Chadha (1989)

Trabajos de Investigación Operativa

In this paper a multiparametric linear fractional functionals program, with parameters appearing only in the objective function, is generated. The optimum solution of this parametric program is supposed to satisfy the constraints as equations only. It is also shown that the set of parameters forms a convex polyhedron.

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