The development of algorithms for semide nite programming is an active research area, based on extensions of interior point methods for linear programming. As semide nite programming duality theory is weaker than that of linear programming, only partial information can be obtained in some cases of infeasibility, nonzero optimal duality gaps, etc. Infeasible start algorithms have been proposed w...

This paper generalizes the Max-Flow Min-Cut (MFMC) theorem from the setting of numerical capacities to cellular sheaves of semimodules on directed graphs. Motivating examples of semimodules include probability distributions, multicommodity capacity constraints, and logical propositions. Directed algebraic topology provides the tools necessary for capturing the salient information in such a gene...

Single Machine Scheduling Problems with Release Dates (SMSP) concern the optimal allocation of a set of jobs on a single machine, that cannot process more than one job at a time. Each job is ready for processing at a release date and it has to be processed without interruption. The goal is to minimize the total weighted completion time of the jobs. In this paper the time-indexed formulation is ...

The paper presents an approach to bi-level programming using a duality gap-penalty function format. A new exact penalty function exists for obtaining a global optimal solution for the linear case, and an algorithm is given for doing this, making use of some new theoretical properties. For each penalty parameter value, the central optimisation problem is one of maximising a convex function over ...

Practical scheduling problems typically require decisions without full information about the outcomes of those decisions. Yields, resource availability, performance, demand, costs, and revenues may all vary. Incorporating these quantities into stochastic scheduling models often produces difficulties in analysis that may be addressed in a variety of ways. In thii paper, we present results based ...

in this paper, we try to determine the status of the relation between dahr world and matrial world. the conclusion shows the subjective duality and objective unity of dahr and material entities. two interpretations of this duality can be suggested. in the first interpretation, this unity, and the duality supposed, are explained on the basis of different intellectual cognition of immaterial and ...

The main aim of this paper is to deal with a fuzzy version of Farkas lemma involving trapezoidal fuzzy numbers. In turns to that the fuzzy linear programming and duality theory on these problems can be used to provide a constructive proof for Farkas lemma. Keywords Farkas Lemma, Fuzzy Linear Programming, Duality, Ranking Functions.

In this paper, we establish weak and strong duality theorems for a pair of multiobjective symmetric dual problems. This removes several omissions in the paper "Symmetric and self duality in vector optimization problem, Applied Mathematics and Computation 183 (2006) 1121-1126".

In this paper we use results on reducibility, localization and duality for the Almost Mathieu operator, (Hb,φx)n = xn+1 + xn−1 + b cos (2πnω + φ) xn on l2(Z) and its associated eigenvalue equation to deduce that for b 6= 0,±2 and ω Diophantine the spectrum of the operator is a Cantor subset of the real line. This solves the so-called “Ten Martini Problem” for these values of b and ω. Moreover, ...