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On the Stochastic Maximum Principle
SIAM Journal on Control and Optimization, 1978A representation of the adjoint process, which appears in a general version of the maximum principle for control systems described by Girsanov solutions of stochastic differential equations, is given in terms of the linearization of the state equation.
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A Stochastic Maximum Principle
SIAM Journal on Control and Optimization, 1976The major theorem of this paper is very closely parallel to the classical Pontryagin maximum principle. The classical case, very roughly stated, says that if $u(t)$ is a control function which has an associated trajectory $x(t)$, then there is a function $H(v,x,t)$ such that $u(t)$ is optimal only if for each t and for all v in the control set, \[H(u(t)
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Aleksandrov maximum principle and bony maximum principle for parabolic equations
Acta Mathematicae Applicatae Sinica, 1985The author simplifies the proof of the Aleksandrov maximum principle for parabolic equations given by Krylov and obtains finer results. He further proves the Bony maximum principle for parabolic equations by using the above results.
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1996
Our study thus far points to the maximum principle as the fundamental principle of optimality and identifies the symplectic structure and the associated Hamiltonian formalism as the main theoretical ingredients required for its proper understanding. In this chapter we shall take that direction to its natural end and ultimately arrive at a geometric ...
V. N. Afanas’ev +2 more
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Our study thus far points to the maximum principle as the fundamental principle of optimality and identifies the symplectic structure and the associated Hamiltonian formalism as the main theoretical ingredients required for its proper understanding. In this chapter we shall take that direction to its natural end and ultimately arrive at a geometric ...
V. N. Afanas’ev +2 more
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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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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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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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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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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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