In this paper we propose two algorithms for solving both unweighted and weighted constrained two-dimensional two-staged cutting stock problems. The problem is called two-staged cutting problem because each produced (sub) optimal cutting pattern is realized by using two cut-phases.

Sequential meta heuristic implementations for the irregular stock-cutting problem have highlighted a number of common problems. The implementation in this paper adopts a hybrid tabu search approach that incorporates two very different optimisation routines which utilise alternative neighborhoods...

In this paper we study the concepts of equilibrium and optimum in static transportation networks with elastic and non-elastic demands. The main mathematical tool of our paper is the theory of variational inequalities. We demonstrate that this theory is useful for proving the existence theorems....

We present a convex conic relaxation for a problem of maximising an indefinite quadratic form over a set of convex constraints on the squared variables. We show that for all these problems we get at least 12/37 relative accuracy of the approximation. In the second part of the paper we derive the...

We propose an alternative approach to stochastic programming based on Monte-Carlo sampling and stochastic gradient optimization. The procedure is by essence probabilistic and the computed solution is a random variable.

In facility layout problems, a major concern is the optimal design or remodeling of the facilities of an organization. The decision maker's objective is to arrange the facility in an optimal way, so that the interaction among functions (i.e. machines, inventories, persons) and places (i.e....

In this paper we study special barrier functions for the convex cones, which are the sum of a self-concordant barrier for the cone and a positive-semidefinite quadratric form. We show that the central path of these augmented barrier functions can be traced with linear speed. We also study the...

A new concept is proposed for linking algebraic modeling languages and the structure exploiting solver.

In optimization, objective functions which are both pseudoconvex and pseudoconcave have extensively been studied. Generalizing these results, we characterize pseudomonotone maps F where also -F is pseudomonotone and explore their properties in variational inequality problems. In particular, we...

Duality is studied for an abstract equilibrium problem which includes, among others, optimization problems and variational inequality problems. Follwing different schemes, various duals are proposed and primal-dual relationships are established under certaing generalized convexity and...