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Leonid Faybusovich (leonid.faybusovich.1nd.edu) Abstract: We consider primaldual algorithms for certain types of infinitedimensional optimization problems. Our approach is based on the generalization of the technique of finitedimensional Euclidean Jordan algebras to the case of infinitedimensional JBalgebras of finite rank. This generalization enables us to develop polynomialtime primaldual algorithms for ``infinitedimensional secondorder cone programs.'' We consider as an example a longstep primaldual algorithm based on the NesterovTodd direction. It is shown that this algorithm can be generalized along with complexity estimates to the infinitedimensional situation under consideration. An application is given to an important problem of control theory: multicriteria analytic design of the linear regulator. The calculation of the NesterovTodd direction requires in this case solving one matrix differential Riccati equation plus solving a finitedimensional system of linear algebraic equations on each iteration. The size of this algebraic system is $m+1$ by $m+1$, where $m$ is a number of quadratic performance criteria. Keywords: Interiorpoint algorithms, primaldual algorithms, secondorder cone programming, infinitedimensional problems, control theory Category 1: Linear, Cone and Semidefinite Programming Category 2: Applications  Science and Engineering (Control Applications ) Citation: Research Memorandum No. 821, The Institute of Statistical Mathematics, 467 MinamiAzabu, Minatoku, Tokyo 1068569 Japan, November 2001 (Revised: December 2001 and November 2002), To appear in Mathematical Programming. Download: [PDF] Entry Submitted: 03/31/2003 Modify/Update this entry  
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