A finite steps algorithm for solving convex feasibility problems |
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| Authors: | M Ait Rami U Helmke J B Moore |
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| Institution: | (1) Department of Mathematics, University of Würzburg, Am Hubland, 97074 Würzburg, Germany;(2) Department of Information Engineering, Research School of Information Sciences and Engineering, Australian National University, Canberra, ACT, 0200, Australia |
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| Abstract: | This paper develops a new variant of the classical alternating projection method for solving convex feasibility problems where
the constraints are given by the intersection of two convex cones in a Hilbert space. An extension to the feasibility problem
for the intersection of two convex sets is presented as well. It is shown that one can solve such problems in a finite number
of steps and an explicit upper bound for the required number of steps is obtained. As an application, we propose a new finite
steps algorithm for linear programming with linear matrix inequality constraints. This solution is computed by solving a sequence
of a matrix eigenvalue decompositions. Moreover, the proposed procedure takes advantage of the structure of the problem. In
particular, it is well adapted for problems with several small size constraints. |
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| Keywords: | Convex optimization Linear matrix inequality Eigenvalue problem Alternating projections |
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