Differential stability in infinite-dimensional nonlinear programming

Lempio, Frank; Maurer, Helmut

doi:10.1007/bf01442889

Cited by 81 publications

(29 citation statements)

References 9 publications

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“…[] Note that (4.6) is known in the sensitivity analysis of optinrization problems in more general cases (see, e.g., [5], [12], [17], and [181). Using (4.6) and Theorem 4.1, for any {/3,}~,0, such that (4:2b) holds, we have…”

Section: F°(h+ Ag) = F°(h) + A(dh~(z~ M H) G) + O(a)mentioning

confidence: 99%

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Sensitivity analysis of optimization problems in Hilbert space with application to optimal control

Malanowski

1990

Appl Math Optim

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Abstract.A family of optimization problems in a Hilbert space depending on a vector parameter is considered. It is assumed that the problems have locally isolated local solutions. Both these solutions and the associated Lagrange multipliers are assumed to be locally Lipschitz continuous functions of the parameter. Moreover, the assumption of the type of strong second-order sufficient condition is satisfied.It is shown that the solutions are directionally differentiable functions of the parameter and the directional derivative is characterized. A secondorder expansion of the optimal-value function is obtained. The abstract results are applied to state and control constrained optimal control problems for systems described by nonlinear ordinary differential equations with the control appearing linearly.

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Section: F°(h+ Ag) = F°(h) + A(dh~(z~ M H) G) + O(a)mentioning

confidence: 99%

“…In the case of optimization problems in Hilbert spaces the sensitivity results are far less complete. They mainly concern the optimal value function (see, e.g., [5] and [12]). …”

Section: Introductionmentioning

confidence: 99%

Sensitivity analysis of optimization problems in Hilbert space with application to optimal control

Malanowski

1990

Appl Math Optim

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“…Differentiable perturbations of infinite-dimensional optimization problems are considered in Lempio/Maurer [9]. In this paper, the results of [9] are applied to optimal control problems with perturbations in the objective function, dynamics, final conditions and state constraints.…”

Section: Introductionmentioning

confidence: 99%

“…This paper deals with optimal control problems subject to differentiable perturbations in the objective function and constraints. The results of [9] are applied to obtain upper and lower bounds for the directional derivative of the extremal value function as well as necessary and sufficient conditions for the existence of the directional derivative. In particular, the results show the close connection between the multipliers of the Minimum Principle and the sensitivity of the optimal value with respect to perturbations.…”

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confidence: 99%

Differential stability in optimal control problems

Maurer

1979

Appl Math Optim

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Abstract. This paper deals with optimal control problems subject to differentiable perturbations in the objective function and constraints. The results of [9] are applied to obtain upper and lower bounds for the directional derivative of the extremal value function as well as necessary and sufficient conditions for the existence of the directional derivative. In particular, the results show the close connection between the multipliers of the Minimum Principle and the sensitivity of the optimal value with respect to perturbations.

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“…We shall apply modern perturbation theory for the abstract programme (P) of §2, see e.g. Lempio and Maurer (1980), to study the nonanticipative constraint multiplier process p' corresponding to the chosen optimal policy ~O for (RP) . Of interest are perturbations to the nonanticipative constraints (2.3) of the form We first establish that this marginal EVPI process e' --like the optimal policy process ~O itself--is adapted to the observation process ~ .…”

Section: The Marginal Expected Value Of Perfect Information Supermartmentioning

confidence: 99%

The expected value of perfect information in the optimal evolution of stochastic systems

Dempster

Stochastic Differential Systems

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PREFACEMethodological research into optimization problems and techniques has a long history in the System and Decision Sciences Program at IIASA. Most recently, effort -of which this paper forms a part -has concentrated on the analysis of stochastic systems.For a very general model of a stochastic optimization problem with an infinite planning horizon in discrete time, the author analyzes the stochastic process describing the marginal expected value of perfect information (EVPI) about the future of the system. He demonstrates two intuitively obvious properties of this marginal EVPI process: that its values are completely predictable at each actual decision point and that its expected values tend to decline over the future since information is potentially worth more the sooner it is available. The author is currently working on continuous time analogs of these results, which are unfortunately fraught with technical difficulties.This work should be viewed as a theoretical prolegomenon to computational studies aimed at estimating the value of perfect or partial information in the control of stochastic systems. The central observation here is that the extra complexity and computational burden of introducing random parameters into planning or control models may sometimes be unnecessary. The (marginal) EVPI at decision points is the natural measure by which their modeling efficacy can be evaluated.

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Differential stability in infinite-dimensional nonlinear programming

Cited by 81 publications

References 9 publications

Sensitivity analysis of optimization problems in Hilbert space with application to optimal control

Sensitivity analysis of optimization problems in Hilbert space with application to optimal control

Differential stability in optimal control problems

The expected value of perfect information in the optimal evolution of stochastic systems

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