Introductory optimization dynamics: optimal control with economics and management applications
This book presents the Calculus of Variations and OptimalControl Theory illustrating the analysis with examples fromEconomics and Management Science. Topics are treated in thesimplest possible way. Students are takenfrom scratch to afairly good mastery of these dynamic optimisation tools forthe purpose of reading the literature and doing researchrequiring these tools.The most important features of the book are the simplicityand thoroughness of presentation. Students working at thebook systematically will acquire a fairly good knowledge ofthe field and, knowing how results have been derived, theywould be in a position to apply, modify and even extendthese standard results to the problems under investigation.The new edition has two new chapters, Chapter 11 onDifferential Games, which would be useful for studentsworking in Industrial Organisation, and Chapter 12 onStability of Optimal Control, which contains new results.
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THE CALCULUS OF VARIATIONS
Particular Cases of the Euler Equation
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assumed assumption Ax(t bang bang-bang bang-bang control bifurcation boundary conditions Calculus of Variations chapter Clearly coefficient concave Consider the problem consumption utility control variables convex cost curvature matrix curve defined determined differential game discussed dynamic system e~rt economic applications eigen values Euler equation gives examined example extremum given Hamiltonian hence implies inequality constraints integration investment labour Lemma Liapunov function linear Linear Regulator marginal utility maximization problem maximize the present minimize minimum n-vector Nash equilibrium necessary conditions neo-classical Note objective functional obtained Optimal Control theory optimal economic growth Optimal Growth Model output parameter path payoff phase diagram player Pontryagin's Pontryagin's Maximum Principle positive definite present value production function saddle point satisfied scalar singular control solution solving strategies structural stability Substituting sufficient conditions switching function Theorem transversality conditions unique unspecified unstable utility function vanishes vector Weierstrass