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arXiv · 1003.4608

Moment and SDP relaxation techniques for smooth approximations of problems involving nonlinear differential equations

Martin Mevissen·Jean-Bernard Lasserre·Didier Henrion
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Abstract

Combining recent moment and sparse semidefinite programming (SDP) relaxation techniques, we propose an approach to find smooth approximations for solutions of problems involving nonlinear differential equations. Given a system of nonlinear differential equations, we apply a technique based on finite differences and sparse SDP relaxations for polynomial optimization problems (POP) to obtain a discrete approximation of its solution. In a second step we apply maximum entropy estimation (using moments of a Borel measure associated with the discrete solution) to obtain a smooth closed-form approximation. The approach is illustrated on a variety of linear and nonlinear ordinary differential equations (ODE), partial differential equations (PDE) and optimal control problems (OCP), and preliminary numerical results are reported.

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Martin Mevissen, Jean-Bernard Lasserre, Didier Henrion. 2010-03-24. Moment and SDP relaxation techniques for smooth approximations of problems involving nonlinear differential equations. https://arxiv.org/abs/1003.4608

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