Introductory Optimization Dynamics: Optimal Control with Economics and Management ApplicationsThis book presents the Calculus of Variations and Optimal Control Theory illustrating the analysis with examples from Economics and Management Science. Topics are treated in the simplest possible way. Students are takenfrom scratch to a fairly good mastery of these dynamic optimisation tools for the purpose of reading the literature and doing research requiring these tools. The most important features of the book are the simplicity and thoroughness of presentation. Students working at the book systematically will acquire a fairly good knowledge of the field and, knowing how results have been derived, they would be in a position to apply, modify and even extend these standard results to the problems under investigation. The new edition has two new chapters, Chapter 11 on Differential Games, which would be useful for students working in Industrial Organisation, and Chapter 12 on Stability of Optimal Control, which contains new results. |
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assumed bang-bang bang-bang control boundary conditions c₂ Calculus of Variations capital chapter Clearly concave Consider the problem consumption utility control variables convex curve defined determined differential equation discount dt subject dx(T dynamic system E-function economic applications eigen values equilibrium Euler equation gives example extremal extremum given Hamiltonian hence implies inequality constraints initial integration investment isoperimetric Jacobi condition Legendre condition Lemma linear marginal utility matrix maximize Maximum Principle minimization problem minimum mixed strategies n-vectors Nash Nash equilibrium necessary conditions Note objective functional obtained Optimal Control problem optimal growth output P₁ P₂ P₂(t payoff player Pontryagin's Pontryagin's Maximum Principle positive definite Riccati equation saddle point satisfied scalar singular control solution stability Stackelberg strategies Substitution sufficient conditions Theorem transversality conditions unspecified vanish vector ән นน