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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....
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...
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...
The problem of a thin elastic plate, deflection of which is limited below by a rigid obstacle is solved. Using Ahlin's and Ari-Adini's elements on rectangles, the convergence is established and SOR method with constraints is proposed for numerical solution.
Round-off error analysis of the gradient method.
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.
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.
Studying a critical value function in parametric nonlinear programming, we recall conditions guaranteeing that is a function and derive second order Taylor expansion formulas including second-order terms in the form of certain generalized derivatives of . 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....
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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