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Abstract: We describe a potential reduction method for convex optimization problems involving matrix inequalities. The method is based on the theory developed by Nesterov and Nemirovsky and generalizes Gonzaga and Todd's method for linear programming. A worst-case analysis shows that the number of iterations grows as the square root of the problem size, but in practice it appears to grow more slowly. As in other interior-point methods the overall computational effort is therefore dominated by the... (Update)
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BibTeX entry: (Update)
L. Vandenberghe and S. Boyd, "A primal-dual potential reduction method for problems involving matrix inequalities," Mathematical Programming, Series B 69 (1995) 205--236. http://citeseer.ist.psu.edu/vandenberghe95primaldual.html More
@techreport{ vandenberghe93primaldual,
author = "L. Vandenberghe and S. Boyd",
title = "Primal--dual potential reduction method for problems involving matrix inequalities",
month = "January",
address = "Stanford, CA~94305, USA",
year = "1993",
url = "citeseer.ist.psu.edu/vandenberghe95primaldual.html" }
Citations (may not include all citations):529 Linear Matrix Inequalities in System and Control Theory (context) - Boyd, Ghaoui et al. - 1994
79 Iterative solution of problems of linear and quadratic progr.. (context) - Dikin - 1967
66 Method of centers for minimizing generalized eigenvalues - Boyd, Ghaoui - 1993
60 Combinatorial optimization with interior point methods and s.. (context) - Alizadeh - 1991 ACM
43 Generalized eigenproblem algorithms and software for algebra.. (context) - Arnold, Laub - 1984
35 An implementation of Karmarkar's algorithm for linear progra.. - Adler, Resende et al. - 1989
12 Optimization over the positive-definite cone: interior point.. (context) - Alizadeh - 1992
11 On systems of linear inequalities in Hermitian matrix variab.. (context) - Bellman, Fan - 1963
8 A combined phase I phase II scaled potential algorithm for l.. (context) - Anstreicher - 1991
2 Interior point polynomial time method for truss topol- ogy d.. (context) - Tal, Nemirovskii - 1992
1 A nonlinear programlning problem in statistics (educational .. (context) - Fletcher - 1981
1 A large-step analytic center method for a class of smooth co.. (context) - Den Hertog, Roos et al.
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