Berkovitz, Leonard David 1924Overview
Publication Timeline
Most widely held works by
Leonard David Berkovitz
Optimal control theory
by Leonard David Berkovitz
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Book
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16 editions published in 1974 in English and Undetermined and held by 602 WorldCat member libraries worldwide
Convexity and optimization in R [superscript n]
by Leonard David Berkovitz
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Book
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15 editions published between 2001 and 2003 in English and held by 329 WorldCat member libraries worldwide "This book presents the mathematics of finite dimensional constrained optimization problems. It provides a basis for the further mathematical study of convexity, of more generalized optimization problems, and of numerical algorithms for the solution of finite dimensional optimization problems. For readers who do not have the requisite background in real analysis, the author provides a chapter covering this material. The text features abundant exercises and problems designed to lead the reader to a fundamental understanding of the material." "A detailed bibliography is included for further study and an index offers quick reference. Suitable as a text for both graduate and undergraduate students in mathematics and engineering, this accessible text is written from extensively classtested notes."Jacket
Nonlinear optimal control theory
by Leonard David Berkovitz
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10 editions published between 2011 and 2013 in English and held by 199 WorldCat member libraries worldwide "Preface This book is an introduction to the mathematical theory of optimal control of processes governed by ordinary differential and certain types of differential equations with memory. The book is intended for students, mathematicians, and those who apply the techniques of optimal control in their research. Our intention is to give a broad, yet relatively deep, concise and coherent introduction to the subject. We have dedicated an entire chapter for examples. We have dealt with the examples pointing out the mathematical issues that one needs to address. The first six chapters can provide enough material for an introductory course in optimal control theory governed by differential equations. Chapters 3, 4, and 5 could be covered with more or less details in the mathematical issues depending on the mathematical background of the students. For students with background in functional analysis and measure theory Chapter 7 can be added. Chapter 7 is a more mathematically rigorous version of the material in Chapter 6. We have included material dealing with problems governed by integrodifferential and delay equations. We have given a unified treatment of bounded state problems governed by ordinary, integrodifferential, and delay systems. We have also added material dealing with the HamiltonJacobi Theory. This material sheds light on the mathematical details that accompany the material in Chapter 6"
A dynamic programming approach to the nonparametric problem in the calculus of variations
by Leonard David Berkovitz
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Book
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2 editions published in 1964 in English and held by 15 WorldCat member libraries worldwide This memorandum presents an approach to the nonparametric simple problem of the calculus of variations that is in the spirit of dynamic programming. Under the assumptions that the functions that define minimizing curves exhibit a certain regularity in their behavior, differentiability properties of the optimal value function W are determined. Then the fundamental partial differential equation of dynamic programming is obtained, and the necessary conditions of the calculus of variations, with the exception of Jacobi's condition, are deduced as immediate corollaries. (Author)
A variational approach to differential games
by Leonard David Berkovitz
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Book
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3 editions published in 1961 in English and held by 12 WorldCat member libraries worldwide
Advances in game theory
by Melvin Dresher
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Book
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1 edition published in 1971 in English and held by 9 WorldCat member libraries worldwide
A survey of certain aspects of the mathematics of control problems
by Leonard David Berkovitz
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Book
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2 editions published in 1962 in English and held by 8 WorldCat member libraries worldwide
Allocation of two types of aircraft in tactical air war : a gametheoretic analysis
by Leonard David Berkovitz
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Book
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1 edition published in 1959 in English and held by 7 WorldCat member libraries worldwide
Variational methods in problems of control and programming
by Leonard David Berkovitz
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Book
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2 editions published in 1961 in English and held by 7 WorldCat member libraries worldwide
The equivalence of some necessary conditions for optimal control in problems with bounded state variables
by Leonard David Berkovitz
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Book
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2 editions published in 1963 in English and held by 7 WorldCat member libraries worldwide The problem of optimal control is considered as earlier studied separately by Gamkrelidze, Berkovitz, and Dreyfus wherein a constraint is placed on the state variables. The three have studied the problem from different viewpoints: Gamkrelidze accounts for the constraint by modifying Pontryagin's maximum principle arguments; Berkovitz applies directly the classical theory developed for the problem of Bolza; and Dreyfus utilizes a dynamic programming approach. The results deduced by the latter approach, in some respects, appear to be unrelated to the Gamkrelidze and Berkovitz results, which are in agreement. It is demonstrated that the two sets of results are actually related. (Author)
A differential game without pure strategy solutions on an open set
by Leonard David Berkovitz
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Book
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2 editions published in 1962 in English and held by 5 WorldCat member libraries worldwide An example is given of a differential game with integral payoff and continuous terminal payoff that does not have a pure strategy solution. The methods and results of a previous approach (A Variational Approach to Differential Games, Rand Corp., Memorandum RM2772, 1961) are used to establish the nonexistence of pure strategies. (Author)
On control problems with bounded state variables
by Leonard David Berkovitz
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Book
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1 edition published in 1962 in English and held by 4 WorldCat member libraries worldwide
Edward James McShane : May 10, 1904June 1, 1989
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Book
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1 edition published in 2001 in English and held by 4 WorldCat member libraries worldwide
A game theory analysis of tactical air war
by Leonard David Berkovitz
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Book
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1 edition published in 1959 in English and held by 3 WorldCat member libraries worldwide
A variational approach to differential games
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Book
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1 edition published in 1961 in English and held by 1 WorldCat member library worldwide A class of differential games having pure strategy solutions is investigated by means of results and techniques from the calculus of variations. These games are related to two Bolza problems with differential inequalities as added side constraints. Necessary conditions that must hold along an optimal path are derived from the theory of the related Bolza problems. These conditions are (1) a multiplier rule, together with transversality conditions and jump conditions, (2) a local minmax condition that is related to the Weierstrass condition, and (3) an analogue of the Clebsch condition. The continuity and differentiability pp yty properties of the value of the game are derived. It is shown that, wherever the value is differentiable, it satisfies an analogue of the HamiltonJacobi equation. Sufficient conditions are given in terms of the notion of a field and of a local minmax condition. (Author)
On differential games with integral payoff
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Book
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1 edition published in 1955 in English and held by 1 WorldCat member library worldwide Methods of the calculus of variations were employed to obtain necessary conditions that differential games of a certain type have a saddlepoint. By strengthening the necessary conditions, sufficient conditions for the existence of a saddlepoint and a method of constructing the saddlepoint were derived. (Author)
On control problems with bounded state variables
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Book
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1 edition published in 1962 in English and held by 1 WorldCat member library worldwide Id ntifiers: Problem solving. Control problems are studied in which constraints that are independent of the control are imposed on the state variables. Necessary conditions that hold along an optimal trajectory are derived in a relatively simple fashion from known results in the calculus of variations. These results had been obtained by Gambrelidze in a different fashion. (Author)
The implications of some gametheoretic analyses for war gaming
by Leonard David Berkovitz
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Book
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1 edition published in 1960 in English and held by 1 WorldCat member library worldwide
A multimove allocation game
by Leonard David Berkovitz
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Book
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1 edition published in 1958 in English and held by 1 WorldCat member library worldwide
A penalty function proof of maximum principle
by Leonard David Berkovitz
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Book
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1 edition published in 1975 in English and held by 1 WorldCat member library worldwide more
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Associated Subjects
Air warfareMathematical models Automatic control Calculus of variations Canada College administrators College teachers Control theory Convex sets Editors Educational assistance Functions of bounded variation Functions of real variables Games of strategy (Mathematics) Game theory Industrial managementMathematical models Mathematical optimization Mathematicians Mathematics McShane, E. J.(Edward James), Nonlinear control theory Nonlinear theories Research Scientists United States War games War gamesMathematical models

Alternative Names
Berkovitz, L. D.
Berkovitz, Leonard D.
Berkovitz, Leonard David
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