Variational Methods In Optimization by Donald R. Smith
A concise graduate-level treatment of variational techniques for solving optimization problems in function spaces, building the necessary functional-analytic framework (Sobolev spaces, weak derivatives) and presenting direct methods for existence and regularity of minimizers. The text develops Euler–Lagrange necessary conditions, constrained variational problems (Lagrange multipliers and variational inequalities), convexity and duality concepts, and illustrates the theory with boundary-value and mechanics applications to connect abstract results with practical solution methods.
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