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Olivier Devolder (Olivier.devolderuclouvain.be) Abstract: We solve a class of convex infinitedimensional optimization problems using a numerical approximation method that does not rely on discretization. Instead, we restrict the decision variable to a sequence of finitedimensional linear subspaces of the original infinitedimensional space and solve the corresponding finitedimensional problems in a efficient way using structured convex optimization techniques. We prove that, under some reasonable assumptions, the sequence of these optimal values converges to the optimal value of the original infinitedimensional problem and give an explicit description of the corresponding rate of convergence. Keywords: infinitedimensional optimization, polynomial approximation, semidefinite programming, positive polynomials, optimization in normed spaces, continuous linear programs, infinite programming Category 1: Infinite Dimensional Optimization Category 2: Convex and Nonsmooth Optimization (Convex Optimization ) Citation: Solving Infinitedimensional Optimization Problems by Polynomial Approximation, Olivier Devolder, François Glineur, Yurii Nesterov, in Recent Advances in Optimization and its Applications in Engineering, Springer, 2010, pp. 3140. http://dx.doi.org/10.1007/9783642125980_3 Download: [PDF] Entry Submitted: 08/03/2010 Modify/Update this entry  
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