NUMERICAL SOLUTION OF A CLASS OF NON-CONVEX VARIATIONAL PROBLEMS BY SQP

ABSTRACT Non-convex variational problems can be solved numerically by sequential quadratic programming (SQP), after relaxation by means of Young measures. The approximate solutions obtained by SQP converge weakly to the solution of the relaxed problem. Strong convergence is provided by compact imbedding of the space of feasible mappings due to assumptions on the growth of the involved integrand. An illustrative two-dimensional example with a known exact solution is included.

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