This monograph studies optimization problems for rigid punches in elastic media and for high-speed penetration of rigid strikers into deformed elastoplastic, concrete, and composite media using variational calculations, tools from functional analysis, and stochastic and min-max (guaranteed) optimization approaches with incomplete data. The book presents analytical and numerical results developed by the authors during the last ten years.ContentsPart I: Quasi-statics of contact interactionOptimal contact pressure and optimal punch shapeInfluence of forces applied outside contact regionShape optimization of punch moving with frictionOptimization in contact problems under incomplete dataApplication of probabilistic dataMinimization of material wearMultiobjective optimization of contact pressure, wear of material, and energy dissipationPart II: High-speed penetration into deformable mediumOptimization of impactor shapeStrikers of nonaxisymmetric optimal shapeMultiobjective optimization of rigid shellOptimization of truncated rotating strikersPenetration into solid medium under strength constraintsSome problems of global multipurpose structural optimizationAnalytical and numerical estimations of optimal parameters of layered slabStriker shape optimization using condition of minimal ballistic limit velocity for layered slabsPart III: AppendicesNonadditive functionals and extremum conditionsMultivariant estimation of functionals and their sensitivityBasic ideas of multicriteria optimizationEvolutionary algorithm of global optimization