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On a dual network exterior point simplex type algorithm and its computational behavior

George Geranis, Konstantinos Paparrizos, Angelo Sifaleras (2012)

RAIRO - Operations Research - Recherche Opérationnelle

The minimum cost network flow problem, (MCNFP) constitutes a wide category of network flow problems. Recently a new dual network exterior point simplex algorithm (DNEPSA) for the MCNFP has been developed. This algorithm belongs to a special “exterior point simplex type” category. Similar to the classical dual network simplex algorithm (DNSA), this algorithm starts with a dual feasible tree-solution and after a number of iterations, it produces a solution that is both primal and dual feasible, i.e....

On a dual network exterior point simplex type algorithm and its computational behavior∗

George Geranis, Konstantinos Paparrizos, Angelo Sifaleras (2012)

RAIRO - Operations Research

The minimum cost network flow problem, (MCNFP) constitutes a wide category of network flow problems. Recently a new dual network exterior point simplex algorithm (DNEPSA) for the MCNFP has been developed. This algorithm belongs to a special “exterior point simplex type” category. Similar to the classical dual network simplex algorithm (DNSA), this algorithm starts with a dual feasible tree-solution and after a number of iterations, it produces a...

On Newton's polygons, Gröbner bases and series expansions of perturbed polynomial programs

Konstantin Avrachenkov, Vladimir Ejov, Jerzy A. Filar (2006)

Banach Center Publications

In this note we consider a perturbed mathematical programming problem where both the objective and the constraint functions are polynomial in all underlying decision variables and in the perturbation parameter ε. Recently, the theory of Gröbner bases was used to show that solutions of the system of first order optimality conditions can be represented as Puiseux series in ε in a neighbourhood of ε = 0. In this paper we show that the determination of the branching order and the order of the pole (if...

On optimizing a maximin nonlinear function subject to replicated quasi-arborescence-like constraints.

Laureano F. Escudero (1985)

Trabajos de Estadística e Investigación Operativa

In this paper we present the motivation for using the Truncated Newton method in an algorithm that maximises a non-linear function with additional maximin-like arguments subject to a network-like linear system of constraints. The special structure of the network (so-termed replicated quasi-arborescence) allows to introduce the new concept of independent superbasic sets and, then, using second-order information about the objective function without too much computer effort and storage.

On quasi-solution to infeasible linear complementarity problem obtained by Lemke’s method

L. Popov (2004)

Open Mathematics

For a linear complementarity problem with inconsistent system of constraints a notion of quasi-solution of Tschebyshev type is introduced. It’s shown that this solution can be obtained automatically by Lemke’s method if the constraint matrix of the original problem is copositive plus or belongs to the intersection of matrix classes P 0 and Q 0.

On second–order Taylor expansion of critical values

Stephan Bütikofer, Diethard Klatte, Bernd Kummer (2010)

Kybernetika

Studying a critical value function ϕ in parametric nonlinear programming, we recall conditions guaranteeing that ϕ is a C 1 , 1 function and derive second order Taylor expansion formulas including second-order terms in the form of certain generalized derivatives of D ϕ . Several specializations and applications are discussed. These results are understood as supplements to the well–developed theory of first- and second-order directional differentiability of the optimal value function in parametric optimization....

On Solving the Maximum Betweenness Problem Using Genetic Algorithms

Savić, Aleksandar (2009)

Serdica Journal of Computing

In this paper a genetic algorithm (GA) is applied on Maximum Betweennes Problem (MBP). The maximum of the objective function is obtained by finding a permutation which satisfies a maximal number of betweenness constraints. Every permutation considered is genetically coded with an integer representation. Standard operators are used in the GA. Instances in the experimental results are randomly generated. For smaller dimensions, optimal solutions of MBP are obtained by total enumeration. For those...

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