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We analyze in this work a spatio-temporal optimal design problem governed by a linear damped 1-D wave equation. The problem consists in seeking simultaneously the spatio-temporal layout of two isotropic materials and the static position of the damping set in order to minimize a functional depending quadratically on the gradient of the state. The lack of… (More)

- Pablo Pedregal
- 2000

We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control variable can be expressed as polynomials. The essential of this proposal is the transformation of a… (More)

This paper deals with the approximation of systems of differential-algebraic equations based on a certain error functional naturally associated with the system. In seeking to minimize the error, by using standard descent schemes, the procedure can never get stuck in local minima but will always and steadily decrease the error until getting to the solution… (More)

We present a new method for micromagnetics based on replacing the nonlocal total energy of magnetizations by a new local energy for divergence-free fields and then studying the dual Legendre functional of this new energy restricted on gradient fields. We establish a Fenchel-type duality principle relevant to the minimization for these problems. The dual… (More)