A proximal point algorithm for control approximation problems

Benker, Hans; Hamel, Andreas H.; Tammer, Christiane

doi:10.1007/bf01194548

Cited by 13 publications

(10 citation statements)

References 12 publications

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“…(P): f(x,u) = E \x(r} T Mx(r] + £(x(t) T Tx(t) + u(t) T Au(t))dt\ -» Min\ (1) under constraints: (i) the control process u(·) is a ^* r adapted stochastic process with values in IR m which has to satisfy control restrictions (A2) G is a compact subset of R^ and the closure of its interior.…”

Section: F(u) = F (X(t) T Tx(t) + U(t} T Ku(t}}dt + X(t) T Mx(t) -> Minimentioning

confidence: 99%

“…(10) ueR 1 Q Taking into consideration that the function in braces is convex with respect to u the condition (10) is equivalent to …”

Section: Theorem 2 Assume (Ali) -(Al4) (A21) and (A22') And Use mentioning

confidence: 99%

“…Now we will construct a proximal point algorithm in order to solve the inclusion (11) using the approach in [1] which is based on the papers [5] and [2].…”

Section: Proximal Point Algorithmmentioning

confidence: 99%

See 2 more Smart Citations

Proximal Point Algorithm for an Approximated Stochastic Optimal Control Problem

Grecksch¹,

Heyde²,

Tammer³

2000

Monte Carlo Methods and Applications

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Section: F(u) = F (X(t) T Tx(t) + U(t} T Ku(t}}dt + X(t) T Mx(t) -> Minimentioning

confidence: 99%

“…(10) ueR 1 Q Taking into consideration that the function in braces is convex with respect to u the condition (10) is equivalent to …”

Section: Theorem 2 Assume (Ali) -(Al4) (A21) and (A22') And Use mentioning

confidence: 99%

See 1 more Smart Citation

Proximal Point Algorithm for an Approximated Stochastic Optimal Control Problem

Grecksch¹,

Heyde²,

Tammer³

2000

Monte Carlo Methods and Applications

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“…Finally, we derive an interactive algorithm for the vectorial control approximation problem using a surrogate parametric optimization problem and taking into account stability results of this special parametric optimization problem (cf. Benker, Hamel, Tammer, 1996;1997).…”

Section: Surrogate Problems For Linear Vector Optimization Problems Effmentioning

confidence: 99%

“…(cf. Benker, Hamel and Tammer, 1996). In order to reformulate the optimality conditions (3)-(5) in a more practical way we introduce a…”

Section: A Suitable Scalarization Of the Vector Optimization Problemmentioning

confidence: 99%

Decision Support for Location Problems in Town Planning

Patz

Spitzner

Tammer

2002

Int Trans Operational Res

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Urban development and town planning need an adequate decision-making process. European cities, in particular, are compact. Urban elements and functions are in a constant state of change. Moreover, the large number of historic buildings and areas means a sensitive and responsible approach must be taken. The aim of this paper is to consider special location problems in town planning. We formulate multi-criteria location problems, derive optimality conditions and present a geometric algorithm and an interactive procedure including a proximal point algorithm for solving multi-criteria location problems. In this paper, we use location theory as a possible method to help determine the location of a children's playground in a newly-built district of Halle, Germany.

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Proximal point method for optimal control processes governed by ordinary differential equations

Azhmyakov

Noriega

2009

Asian Journal of Control

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This paper is concerned with the proximal-based approach to linear and finite-difference approximations of constrained convex optimal control problems. We consider control systems governed by ordinary differential equations in the presence of additional terminal/state inequalities and propose a numerical method derived from the proximal point algorithm. The aim of the paper is to study the convergence properties of the obtained conceptual algorithm and to show that it can be used to compute approximate optimal controls.

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A proximal point algorithm for control approximation problems

Cited by 13 publications

References 12 publications

Proximal Point Algorithm for an Approximated Stochastic Optimal Control Problem

Proximal Point Algorithm for an Approximated Stochastic Optimal Control Problem

Decision Support for Location Problems in Town Planning

Proximal point method for optimal control processes governed by ordinary differential equations

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