A note on approximate solutions in parametric semi-infinite optimization
A note on best constants in discrete inequalities.
A note on direct methods for approximations of sparse Hessian matrices
Necessity of computing large sparse Hessian matrices gave birth to many methods for their effective approximation by differences of gradients. We adopt the so-called direct methods for this problem that we faced when developing programs for nonlinear optimization. A new approach used in the frame of symmetric sequential coloring is described. Numerical results illustrate the differences between this method and the popular Powell-Toint method.
A note on dual approximation algorithms for class constrained bin packing problems
In this paper we present a dual approximation scheme for the class constrained shelf bin packing problem. In this problem, we are given bins of capacity , and items of different classes, each item with class and size . The problem is to pack the items into bins, such that two items of different classes packed in a same bin must be in different shelves. Items in a same shelf are packed consecutively. Moreover, items in consecutive shelves must be separated by shelf divisors of size . In...
A note on dual approximation algorithms for class constrained bin packing problems
In this paper we present a dual approximation scheme for the class constrained shelf bin packing problem. In this problem, we are given bins of capacity 1, and n items of Q different classes, each item e with class ce and size se. The problem is to pack the items into bins, such that two items of different classes packed in a same bin must be in different shelves. Items in a same shelf are packed consecutively. Moreover, items in consecutive shelves must be separated by shelf divisors of size...
A note on economic equilibrium with nonsatiated utility functions
The purpose of this paper is to prove the existence of a Walrasian equilibrium for the Arrow-Debreu and Arrow-Debreu-McKenzie models with positive price vector with nonsatiated utility functions of consumers by using variational inequalities. Moreover, the same technique is used to give an alternative proof of the existence of a Walrasian equilibrium for the Arrow-Debreu and Arrow-Debreu-McKenzie models with nonnegative, nonzero price vector with nonsatiated utility functions.
A Note on Embeddings for the Augmented Lagrange Method
A note on essential components and essential weakly efficient solutions for multiobjective optimization problems.
A Note on Geometry of Polyhedron of Three-index Transportation Problem
A note on Gordan's theorem over cone domains.
A note on minimum-dummy-activities PERT networks
A note on Minty type vector variational inequalities
The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space are introduced....
A note on Minty type vector variational inequalities
The existence of solutions to a scalar Minty variational inequality of differential type is usually related to monotonicity property of the primitive function. On the other hand, solutions of the variational inequality are global minimizers for the primitive function. The present paper generalizes these results to vector variational inequalities putting the Increasing Along Rays (IAR) property into the center of the discussion. To achieve that infinite elements in the image space Y are introduced. Under...
A note on necessary conditions in mathematical programming
A note on operators of deletion and contraction for antichains.
A note on optimality conditions for dual problems to the traveling salesman problem
A note on quasiconvex functions that are pseudoconvex.
In the present note we consider the definitions and properties of locally pseudo- and quasiconvex functions and give a sufficient condition for a locally quasiconvex function at a point x ∈ Rn, to be also locally pseudoconvex at the same point.
A note on resolving the inconsistency of one-sided max-plus linear equations
When a system of one-sided max-plus linear equations is inconsistent, its right-hand side vector may be slightly modified to reach a consistent one. It is handled in this note by minimizing the sum of absolute deviations in the right-hand side vector. It turns out that this problem may be reformulated as a mixed integer linear programming problem. Although solving such a problem requires much computational effort, it may propose a solution that just modifies few elements of the right-hand side vector,...
A Note on Small Linear-Ordering Polytopes.
A note on some separable location problems - a multicriterial approach