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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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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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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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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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Maximum Principles for Nonlinear Fractional Differential Equations in Reliable Space
Progress in Fractional Differentiation and Applications, 2020semanticscholar +1 more source
The Classical Maximum Principle
1977The purpose of this chapter is to extend the classical maximum principles for the Laplace operator, derived in Chapter 2, to linear elliptic differential operators of the form $$Lu \equiv {a^{ij}}\left( x \right){D_{ij}}u + {b^i}\left( x \right){D_i}u + c\left( x \right)u,\quad {a^{ij}} = {a^{ji}},$$ (3.1) where x = (x 1, … , x n ) lies in a ...
David Gilbarg, Neil S. Trudinger
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Maximum principles for some quasilinear elliptic systems
Nonlinear Analysis, 2020S. Leonardi +4 more
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Maximum Principles for k-Hessian Equations with Lower Order Terms on Unbounded Domains
Journal of Geometric Analysis, 2020T. Bhattacharya, Ahmed Mohammed
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