Variational Analysis with Applications in Optimisation and Control

This book focuses on the calculus of variations and related applications which combine tools and methods from partial differential equations with geometrical techniques. More precisely, it is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. It provides the latest developments in multidimensional optimization and optimal control. With various examples and applications to complement and substantiate mathematical developments, the text is a valuable guide for researchers, engineers and students in the field of mathematics, and those working in operations research, optimal control science, artificial intelligence, management science and economics. Dedication Contents Preface Acknowledgement 1 Efficiency conditions in vector variational problems involving higher-order derivatives 2 Controlled signomial dynamical systems as constraints in variational control problems 3 Sufficient conditions of efficiency for a class of vector fractional variational problems 4 Hamilton and Hamilton-Jacobi dynamics of higher-order 5 Necessary and sufficient conditions of efficiency in vector fractional variational control problems 6 Duality results involving (ρ, b)-quasiinvexity for a class of vector fractional variational control problems 7 Geometric optimal control problems 8 On a class of variational control problems 9 Weak sharpness of the solution set associated with an integral variational inequality 10 On efficient solutions associated with a class of PDE-constrained vector variational control problems 11 Modified variational control problems and saddle-point optimality criteria 12 On local and global optimal solutions in variational control problems Bibliography