Results 261 to 270 of about 436,329 (309)
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1972
The values that an analytic function assumes in the different parts of its domain of existence are related to each other : they are connected by analytic continuation and it is impossible to modify the values in one part without inducing a change throughout.
George Pólya, Gabor Szegö
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The values that an analytic function assumes in the different parts of its domain of existence are related to each other : they are connected by analytic continuation and it is impossible to modify the values in one part without inducing a change throughout.
George Pólya, Gabor Szegö
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2007
We consider classical linear and quasilinear elliptic inequalities as well as divergence structure and variational operators, with emphasis on the important topics of comparison results and tangency theorems. This work ultimately applies also to weak solutions in appropriate Sobolev spaces. In order that the book may serve the purposes of reference and
PUCCI, Patrizia, J. SERRIN
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We consider classical linear and quasilinear elliptic inequalities as well as divergence structure and variational operators, with emphasis on the important topics of comparison results and tangency theorems. This work ultimately applies also to weak solutions in appropriate Sobolev spaces. In order that the book may serve the purposes of reference and
PUCCI, Patrizia, J. SERRIN
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1996
In practical problems certain essential constraints are usually imposed on the control set. For such problems the necessary conditions for optimal control stated in the preceding chapter are, in general, not suitable. Necessary conditions for optimality in such problems are furnished by Pontryagin’s maximum principle, which is the subject of this ...
V. N. Afanas’ev +2 more
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In practical problems certain essential constraints are usually imposed on the control set. For such problems the necessary conditions for optimal control stated in the preceding chapter are, in general, not suitable. Necessary conditions for optimality in such problems are furnished by Pontryagin’s maximum principle, which is the subject of this ...
V. N. Afanas’ev +2 more
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2012
This chapter represents the basic concepts of Classical Optimal Control related to the Maximum Principle. The formulation of the general optimal control problem in the Bolza (as well as in the Mayer and the Lagrange) form is presented. The Maximum Principle, which gives the necessary conditions of optimality, for various problems with a fixed and ...
Vladimir G. Boltyanski +1 more
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This chapter represents the basic concepts of Classical Optimal Control related to the Maximum Principle. The formulation of the general optimal control problem in the Bolza (as well as in the Mayer and the Lagrange) form is presented. The Maximum Principle, which gives the necessary conditions of optimality, for various problems with a fixed and ...
Vladimir G. Boltyanski +1 more
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2010
This chapter focuses on a set of optimality conditions known as the Maximum Principle. Many competing sets of optimality conditions are now available, but the Maximum Principle retains a special significance. An early version of the Maximum Principle due to Pontryagin er al.
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This chapter focuses on a set of optimality conditions known as the Maximum Principle. Many competing sets of optimality conditions are now available, but the Maximum Principle retains a special significance. An early version of the Maximum Principle due to Pontryagin er al.
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2001
We present here the most significant results which are customarily grouped under the name of Maximum Principle. It supplies a set of necessary conditions of optimality for a wide class of optimal control problems. Firstly, we give a formal, yet synthetic, description of these problems is given.
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We present here the most significant results which are customarily grouped under the name of Maximum Principle. It supplies a set of necessary conditions of optimality for a wide class of optimal control problems. Firstly, we give a formal, yet synthetic, description of these problems is given.
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1991
The aim of the paper is to give a high order maximum principle for an optimal control problem in the Mayer form with constraints on the endpoint and to discuss its relations with other analogous results. Only smooth time-independent control systems on ℝn will be considered in order to give a simpler exposition.
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The aim of the paper is to give a high order maximum principle for an optimal control problem in the Mayer form with constraints on the endpoint and to discuss its relations with other analogous results. Only smooth time-independent control systems on ℝn will be considered in order to give a simpler exposition.
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1998
The strong maximum principle of E. Hopf says that a solution of an elliptic PDE cannot assume an interior maximum. This leads to further results about solutions of such PDEs, like removability of singularities, gradient bounds, or Liouville’s theorem saying that every bounded harmonic functions defined on all of Euclidean space is constant.
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The strong maximum principle of E. Hopf says that a solution of an elliptic PDE cannot assume an interior maximum. This leads to further results about solutions of such PDEs, like removability of singularities, gradient bounds, or Liouville’s theorem saying that every bounded harmonic functions defined on all of Euclidean space is constant.
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2008
The maximum principle is formulated and proved first for control problems with fixed terminal time. As an illustration, a new derivation of the solution to the linear regulator problem is given. Next the maximum principle for impulse control problems and for time optimal problems are discussed.
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The maximum principle is formulated and proved first for control problems with fixed terminal time. As an illustration, a new derivation of the solution to the linear regulator problem is given. Next the maximum principle for impulse control problems and for time optimal problems are discussed.
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