Simulation of phase combinations in shape memory alloys patches by hybrid optimization methods
Applied Numerical Mathematics
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In nonconvex optimization problems, in particular in nonconvex variational problems, there usually does not exist any classical solution but only generalized solutions which involve Young measures. In this paper, after reviewing briefly the relaxation theory for such problems, an iterative scheme leading to a “sequential linear programming” (=SLP) scheme is introduced, and its convergence is proved by a Banach fixed-point technique. Then an approximation scheme is proposed and analyzed, and calculations of an illustrative 2D “broken-extremal” example are presented.