## Mathematical Systems Theory and Economics I/II: Proceeding of an International Summer School held in Varenna, Italy, June 1–12, 1967The International Summer School on Mathematical Systems Theory and Economics was held at the Villa Monastero in Varenna, Italy, from June 1 through June 12, 1967. The objective of this Summer School was to review the state of the art and the prospects for the application of the mathematical theory of systems to the study and the solution of economic problems. Particular emphasis was given to the use of the mathematical theory of control for the solution of problems in economics. It was felt that the publication of a volume collecting most of the lectures given at the school would show the current status of the application of these methods. The papers are organized into four sections arranged into two volumes: basic theories and optimal control of economic systems which appear in the first volume, and special mathematical problems and special applications which are contained in the second volume. Within each section the papers follow in alphabetical order by author. The seven papers on basic theories are a rather complete representative sample of the fundaments of general systems theory, of the theory of dynamical systems and the theory of control. The five papers on the application of optimal control to economic systems present a broad spectrum of applications. |

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### Contents

2 | |

10 | |

Convex Functions and Duality in Optimization Problems | 117 |

Optimal Control of Economic Systems | 189 |

Dynamic Keynesian Economic Systems Control and Identification | 205 |

On the Controllability of Decentralized Macroeconomic Systems | 221 |

Application of Pontriagins Maximum Principle to Economics | 241 |

Special Mathematical Problems | 293 |

Special Applications | 405 |

Investigations of Organization of Production Processes with Tree | 421 |

Optimum Control and Synthesis of Organizational Structure of Large | 441 |

Optimal Accumulation in a Listian Model | 457 |

Multilevel Approach to the Largescale Control Problem | 481 |

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Mathematical Systems Theory and Economics I/II: Proceeding of an ... H.W. Kuhn,G.P. Szegö No preview available - 1969 |

### Common terms and phrases

algebraic allocation application assume assumptions asymptotically asymptotically stable attractor capital accumulation causality ordering consider constant constraint consumption continuous continuous function control theory convex function convex program convex set coordination corresponding curve decentralized defined definition denote differential equations duality dynamical systems economic equilibrium example exists exp Yt feasible finite function f growth Hamiltonian Hence implies infimum initial input integral interactions inverse optimal problem investment labor Lagrange multiplier Lecture linear locally compact mapping Math mathematical matrix maximize Maximum Principle metric space minimal necessary conditions neighborhood nonlinear obtained optimal control optimum ordinary differential equations output partial results path pattern Pontryagin positive production proof properties Proposition real number respect satisfied solution space stable stationary point structure subset supremum systems theory Theorem topological topological space trajectory unique variables vector vector space weakly invariant zero