Penalty/Barrier Multiplier Algorithm for Semidefinite Programming
Leonid Mosheyev and Michael Zibulevsky
We present a generalization of the Penalty/Barrier Multiplier
algorithm for the semidefinite programming, based on a matrix form of
Lagrange multipliers. Our approach allows to use among others
logarithmic, shifted logarithmic, exponential and a very effective
quadratic-logarithmic penalty/barrier functions. We present dual
analysis of the method, based on its correspondence to a proximal
point algorithm with nonquadratic distance-like function. We give
computationally tractable dual bounds, which are produced by the
Legendre transformation of the penalty function. Numerical results
for large-scale problems from robust control, stable truss topology
design and optimal material design demonstrate high efficiency of the
algorithm.
Preprint, September, 1999
Contact: [email protected]
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