6 research outputs found

    A new primal-dual path-following method for convex quadratic programming

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    The Optimal Set and Optimal Partition Approach to Linear and Quadratic Programming

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    In this chapter we describe the optimal set approach for sensitivity analysis for LP. We show that optimal partitions and optimal sets remain constant between two consecutive transition-points of the optimal value function. The advantage of using this approach instead of the classical approach (using optimal bases) is shown. Moreover, we present an algorithm to compute the partitions, optimal sets and the optimal value function. This is a new algorithm and uses primal and dual optimal solutions. We also extend some of the results to parametric quadratic programming, and discuss differences and resemblances with the linear programming case

    Solving Reduced KKT Systems in Barrier Methods for Linear and Quadratic Programming

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    Solving multiobjective mathematical programming problems with fixed and fuzzy coefficients

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    Many concrete problems, ranging from Portfolio selection to Water resource management, may be cast into a multiobjective programming framework. The simplistic way of superseding blindly conflictual goals by one objective function let no chance to the model but to churn out meaningless outcomes. Hence interest of discussing ways for tackling Multiobjective Programming Problems. More than this, in many real-life situations, uncertainty and imprecision are in the state of affairs. In this dissertation we discuss ways for solving Multiobjective Programming Problems with fixed and fuzzy coefficients. No preference, a priori, a posteriori, interactive and metaheuristic methods are discussed for the deterministic case. As far as the fuzzy case is concerned, two approaches based respectively on possibility measures and on Embedding Theorem for fuzzy numbers are described. A case study is also carried out for the sake of illustration. We end up with some concluding remarks along with lines for further development, in this field.Operations ResearchM. Sc. (Operations Research
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