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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arbitrary assumed boundary conditions C₁ c₂ Calculus of Variations capital chapter Clearly concave constant consumption utility control variables convex cost curve defined determined differential equation Differential Games discount dx(T dynamic system E-function economic applications eigen values equilibrium Euler equation gives example extremum functional J(x given Hamiltonian hence implies inequality constraints integration investment Jacobi condition Liapunov function linear marginal utility Maximum Principle minimize minimum mixed strategies n-vectors Nash Nash equilibrium necessary conditions neo-classical Note objective functional obtained Optimal Control theory optimal growth model output P₁ P₂ parameter payoff phase diagram player Pontryagin's Pontryagin's Maximum Principle positive definite present value production function saddle point satisfied solution Stackelberg strategies Substitution sufficient conditions switching Theorem transversality conditions unspecified vector Weierstrass әк ән นน