Convergence of an Interior Point Algorithm for Continuous Minimax |
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Authors: | B Rustem S Žaković P Parpas |
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Affiliation: | (1) Department of Computing, Imperial College, London, UK |
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Abstract: | We propose an algorithm for the constrained continuous minimax problem. The algorithm uses a quasi-Newton search direction,
based on subgradient information, conditional on maximizers. The initial problem is transformed to an equivalent equality
constrained problem, where the logarithmic barrier function is used to ensure feasibility. In the case of multiple maximizers,
the algorithm adopts semi-infinite programming iterations toward epiconvergence. Satisfaction of the equality constraints
is ensured by an adaptive quadratic penalty function. The algorithm is augmented by a discrete minimax procedure to compute
the semi-infinite programming steps and ensure overall progress when required by the adaptive penalty procedure. Progress
toward the solution is maintained using merit functions. |
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Keywords: | Worst case analysis Continuous minimax algorithms Interior point methods Semi– infinite programming |
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