Analysis of local minima for constrained minimization problems

2014/11/13 by S. J. Bedford, Bedford, S. J.
Mathematics · Computer Science · Engineering · #Advanced Optimization Algorithms Research #Matrix Theory and Algorithms #Topology Optimization in Engineering

paper · pdf · doi:10.48550/arxiv.1411.3595

Abstract

We consider vectorial problems in the calculus of variations with an additional pointwise constraint. Our admissible mappings \bf n:ℝ^k→ ℝ^d satisfy \bf n(x)∈ M, where M is a manifold embedded in Euclidean space. The main results of the paper all formulate necessary or sufficient conditions for a given mapping \bf n to be a weak or strong local minimizer. Our methods involve using projection mappings in order to build on existing, unconstrained, local minimizer results. We apply our results to a liquid crystal variational problem to quantify the stability of the unwound cholesteric state under frustrated boundary conditions.

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