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Double Smoothing Technique For Infinite-dimensional Optimization Problems With Applications To Optimal Control

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Executive Summary

In this paper, the authors propose an efficient technique for solving some infinite-dimensional problems over the sets of functions of time. In this problem, besides the convex point-wise constraints on state variables, they have convex coupling constraints with finite-dimensional image. Hence, they can formulate a finite-dimensional dual problem, which can be solved by efficient gradient methods. They show that it is possible to reconstruct an approximate primal solution. In order to accelerate the schemes, they apply double-smoothing technique. As a result, the method has complexity O(1/? ln 1/?) gradient iterations, where ? is the desired accuracy of the solution of the primal-dual problem.

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