K. Roos
http://repub.eur.nl/ppl/11383/
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http://repub.eur.nl/
RePub, Erasmus University RepositorySensitivity Analysis in (Degenerate) Quadratic Programming
http://repub.eur.nl/pub/1375/
Mon, 01 Jan 1996 00:00:01 GMT<div>A.B. Berkelaar</div><div>B. Jansen</div><div>K. Roos</div><div>T. Terlaky</div>
In this paper we deal with sensitivity analysis in convex quadratic programming, without making assumptions on nondegeneracy, strict convexity of the objective function, and the existence of a strictly complementary solution.
We show that the optimal value as a function of a right--hand side element (or an element of the linear part of the objective) is piecewise quadratic, where the pieces can be characterized by maximal complementary solutions and tripartitions. Further, we investigate differentiability of this function. A new algorithm to compute the optimal value function is proposed. Finally, we discuss the advantages of this approach when applied to mean--variance portfolio
models.Basis- and tripartition identification for quadratic programming and lineair complementary problems; From an interior solution to an optimal basis and viceversa
http://repub.eur.nl/pub/1380/
Mon, 01 Jan 1996 00:00:01 GMT<div>A.B. Berkelaar</div><div>B. Jansen</div><div>K. Roos</div><div>T. Terlaky</div>
Optimal solutions of interior point algorithms for linear and quadratic programming and linear complementarity problems provide maximal complementary solutions. Maximal complementary solutions can be characterized by optimal (tri)partitions. On the other hand, the solutions provided by simplex--based pivot algorithms are given in terms of complementary bases. A basis identification algorithm is an algorithm which generates a complementary basis, starting from any complementary solution.
A tripartition identification algorithm is an algorithm which generates a maximal complementary solution (and its corresponding tripartition), starting from any complementary solution. In linear programming such algorithms were respectively proposed by Megiddo in 1991 and Balinski and Tucker in 1969.
In this paper we will present identification algorithms for quadratic programming and linear complementarity problems with sufficient matrices. The presented algorithms are based on the principal pivot transform and the orthogonality property of basis tableaus.The Optimal Set and Optimal Partition Approach to Linear and Quadratic Programming
http://repub.eur.nl/pub/1394/
Mon, 01 Jan 1996 00:00:01 GMT<div>A.B. Berkelaar</div><div>K. Roos</div><div>T. Terlaky</div>
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.