The Problem of Projecting the Origin of Euclidean Space onto the Convex Polyhedron
- 2 Downloads
This paper is aimed at presenting a systematic exposition of the existing now different formulations for the problem of projection of the origin of the Euclidean space onto the convex polyhedron (PPOCP). We have concentrated on the convex polyhedron given as a convex hull of finitely many vectors of the space. We investigated the reduction of the projection program to the problems of quadratic programming, maximin, linear complementarity, and nonnegative least squares. Such reduction justifies the opportunity of utilizing a much more broad spectrum of powerful tools of mathematical programming for solving the PPOCP. The paper’s goal is to draw the attention of a wide range of research at the different formulations of the projection problem.
Keywords and phrasesprojection convex polyhedron quadratic programming maximin problem complementarity problem nonnegative least squares problem
Unable to display preview. Download preview PDF.
- 16.F. P. Vasil’ev, Numerical Methods for Solving Extremum Problems (Nauka, Moscow, 1980) [in Russian].Google Scholar
- 18.V. A. Daugavet, Numerical Methods of Quadratic Programming (SPb. Gos. Univ., St. Petersburg, 2004) [in Russian].Google Scholar
- 19.G.V. Reklaitis, A. Ravindran, and K.M. Ragsdell, Engineering Optimization: Methods and Applications, 2nd ed. (Wiley, New York, 2006).Google Scholar
- 22.A. Lucia, “Succesive quadratic programming: decompositionmethods,” in Encyclopedia of Optimization, Ed. by C. A. Floudas and P.M. Pardalos (Springer, New York, 2001), pp. 3866–3871.Google Scholar
- 32.K. P. Bennett and E. J. Bredensteiner, “Duality and Geometry in SVM Classifiers,” in Proceedings of the 17th International Conference on Machine Learning, 2000, pp. 57–64.Google Scholar
- 33.F. R. Gantmacher, The Theory ofMatrices (Nauka, Moscow, 1966) [in Russian].Google Scholar
- 38.C. L. Lowson and R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, NJ, 1974).Google Scholar
- 40.D. Chen and R. Plemmons, “Nonnegativity constraints in numerical analysis,” in Proceedings of the Symposium on Birth of Numerical Analysis (Leuven, Belgium, 2007).Google Scholar