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Abstract: We consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices, each of which depends affinely on the decision variables. Although this problem may appear specialized, it is in fact quite general, and includes for example all linear, quadratic, and linear fractional programs. Many problems arising in control theory can be cast in this form. (Update)
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BibTeX entry: (Update)
S. Boyd and L. El Ghaoui. Method of centers for minimizing generalized eigenvalues. Linear Algebra and Applications, ?:?, 1993. http://citeseer.ist.psu.edu/boyd93method.html More
@article{ boyd93method,
author = "Stephen Boyd and Laurent {El Ghaoui}",
title = "Method of Centers for Minimizing Generalized Eigenvalues",
journal = "Linear Algebra and its Applications",
volume = "188/189",
pages = "63--111",
year = "1993",
url = "citeseer.ist.psu.edu/boyd93method.html" }
Citations (may not include all citations):529 Linear matrix inequalities in systems and control theory (context) - Boyd, Ghaoui et al. - 1993
448 A new polynomial-time algorithm for linear programming (context) - Karmarkar - 1984
307 Interior point polynomial methods in convex programming: The.. (context) - Nesterov, Nemirovsky - 1993
172 Nonlinear programming: sequential unconstrained minimization.. (context) - Fiacco, McCormick - 1990
129 A polynomial algorithm in linear programming (context) - Khachiyan - 1979
90 Primal-dual potential reduction method for problems involvin.. - Vandenberghe, Boyd - 1993
83 Linear Controller Design: Limits of Performance (context) - Boyd, Barratt - 1991
79 Iterative solution of problems of linear and quadratic progr.. (context) - Dikin - 1967
64 Interior methods for constrained optimization - Wright - 1992
60 The cutting-plane method for solving convex programs (context) - Kelley - 1960
60 Combinatorial optimization with interior point methods and s.. (context) - Alizadeh - 1991
51 Minimization Methods for Non-differentiable Functions (context) - Shor - 1985
49 Large-scale optimization of eigenvalues - Overton - 1992
49 An interior-point method for minimizing the maximum eigenval.. (context) - Jarre - 1991
48 Self-concordant functions and polynomial time methods in con.. (context) - Nesterov, Nemirovsky - 1990
47 On minimizing the maximum eigenvalue of a symmetric matrix (context) - Overton - 1988
39 Optimality conditions and duality theory for minimizing sums.. - Overton, Womersley - 1993
38 The ellipsoid method: A survey (context) - Bland, Goldfarb et al. - 1981
31 The formulation and analysis of numerical methods for invers.. (context) - Friedland, Nocedal et al. - 1987
30 Semidefinite matrix constraints in optimization (context) - Fletcher - 1985
29 The minimization of certain nondifferentiable sums of eigenv.. (context) - Cullum, Donath et al. - 1975
29 Problem Complexity and Method Efficiency in Optimization (context) - Nemirovsky, Yudin - 1983
23 Resolution of mathematical programming with nonlinear constr.. (context) - Huard - 1967
20 Optimization over positive semidefinite matrices: mathematic.. (context) - Nesterov, Nemirovsky - 1990
20 the sum of the largest eigenvalues of a symmetric matrix (context) - Overton, Womersley - 1992
17 Structured and simultaneous Lyapunov functions for system st.. - Boyd, Yang - 1989
17 Interior-point methods for convex programming (context) - Jarre - 1991
16 An interior point method for generalized linear-fractional p.. (context) - Nesterov, Nemirovsky - 1991
15 A nondifferentiable optimization algorithm for the design of.. (context) - Polak, Wardi - 1982
14 analytical centre (context) - Sonnevend - 1986
13 Optimal design of nonlinear shell structures (context) - Ringertz - 1991
13 Extremal problems on the set of nonnegative definite matrice.. (context) - Shapiro - 1985
12 Combinatorial optimization with semidefinite matrices (context) - Alizadeh - 1992
12 Optimization over the positive-definite cone: interior point.. (context) - Alizadeh - 1992
11 A general approach to polynomial-time algorithms design for .. (context) - Nesterov, Nemirovsky - 1988
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11 Conic formulation of a convex programming problem and dualit.. (context) - Nesterov, Nemirovsky - 1991
11 Linear programming with matrix variables (context) - Craven, Mond - 1981
6 Computing bounds for the structured singular value via an in.. - Balakrishnan, Feron et al. - 1992
6 On maximizing the minimum eigenvalue of a linear combination.. (context) - Allwright - 1989
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5 On maximizing a robustness measure for structured nonlinear .. - Ghaoui, Balakrishnan et al. - 1992
4 Design of stabilizing state feedback for delay systems via c.. - Feron, Balakrishnan et al. - 1992
4 On minimax eigenvalue problems via constrained optimization (context) - Goh, Teo - 1988
4 La m'ethode des centres dans un espace topologique (context) - Lieu, Huard - 1965
4 On minimizing the largest eigenvalue of a symmetric matrix (context) - Fan, Nekooie - 1992
4 the need for special purpose algorithms for minimax eigenval.. (context) - Panier - 1989
4 A quadratically convergent algorithm on minimizing the large.. (context) - Fan - 1992
3 Numerical methods for H 2 related problems (context) - Feron, Balakrishnan et al. - 1992
3 On some efficient interior point methods for nonlinear conve.. (context) - Kortanek, Potra et al. - 1991
3 Applications of analytic centers (context) - Sonnevend - 1991
2 Khachiyan's algorithm for linear programming (context) - G'acs, Lov'asz - 1981
1 On shape optimizing the ratio of the first two eigenvalues o.. - Haeberly - 1991
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