Deterministic and stochastic optimization problems of bolza type in discrete time

Rockafellart, R. T.; Wetst, R. J. B

doi:10.1080/17442508308833276

Cited by 33 publications

(26 citation statements)

References 13 publications

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“…Indeed, Assumptions C and D of [21] require the existence of a μ ∈ L 1 such that |h(x, ω)| ≤ μ(ω) for all x ∈ dom h(·, ω) and that the sets dom h(·, ω) are closed, uniformly bounded and that the projection mappings ω → {x t | x ∈ dom h(·, ω)} are F t -measurable for all t. The following example gives more general conditions in the spirit of the "bounded recourse condition" given in [24].…”

Section: Assumption 1 For Everymentioning

confidence: 99%

Shadow price of information in discrete time stochastic optimization

Pennanen

Perkkiö

2017

Math. Program.

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The shadow price of information has played a central role in stochastic optimization ever since its introduction by Rockafellar and Wets in the mid-seventies. This article studies the concept in an extended formulation of the problem and gives relaxed sufficient conditions for its existence. We allow for general adapted decision strategies, which enables one to establish the existence of solutions and the absence of a duality gap e.g. in various problems of financial mathematics where the usual boundedness assumptions fail. As applications, we calculate conjugates and subdifferentials of integral functionals and conditional expectations of normal integrands. We also give a dual form of the general dynamic programming recursion that characterizes shadow prices of information. The second author is grateful to the Einstein Foundation for the financial support. Keywords B Teemu Pennanen

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Section: Assumption 1 For Everymentioning

confidence: 99%

Shadow price of information in discrete time stochastic optimization

Pennanen

Perkkiö

2017

Math. Program.

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“…Arkin and Evstigneev [1979]. Rockafellar and Wets [1983] and Hiriart-Urruty [1982]. One of our main results in this section conterns turnpike optimality which in the deterministic case may be found in McKenzie (19761 and in stochastic models in, for example, Sethi et al [1992].…”

Section: The Tacticalmentioning

confidence: 64%

Stochastic programming approaches to stochastic scheduling

Birge

Dempstert

1996

J Glob Optim

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Practical scheduling problems typically require decisions without full information about the outcomes of those decisions. Yields, resource availability, performance, demand, costs, and revenues may all vary. Incorporating these quantities into stochastic scheduling models often produces difficulties in analysis that may be addressed in a variety of ways. In thii paper, we present results based on stochastic programming approaches to the hierarchy of decisions in typical stochastic scheduling situations. Our unifying framework allows us to treat all aspects of a decision in a similar framework. We show how views from different levels enable approximations that can overcome nonconvexities and duality gaps that appear in deterministic formulations. In particular, we show that the stochastic program structure leads to a vanishing Lagrangian duality gap in stochastic integer programs as the number of scenarios increases.

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“…Paper [2]. "Deterministic and stochastic optimization problems of Bolya type in discrete time," deals with multistage problems in stochastic programming.…”

Section: Stochastic Programmingmentioning

confidence: 99%

“…Paper [2] seeks to identify structure of a special nature that lends hope in being able to solve such a difficult problem. The emphasis here is on being able to understand what goes on when there is significant number of time periods.…”

Section: Stochastic Programmingmentioning

confidence: 99%

Subgradient Methods in Deterministic and Stochastic Optimization.

Rockafellar¹

1984

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February 27. 1984 Introduction. Research supported by this two-year grant in the period from January, 1982, through December, 1984, has resulted in a total of 11 technical articles and two doctoral theses. These range over several areas of mathematical optimization theory but share the common theme of the development and application of subgradient methods and duality to problems in mathematical programming. Fundamental advances in concept have been made, and in the case of stochastic problems, new techniques of solution have been initiated that may revolutionize the subject. The publications are grouped under the following headings, which will be discussed individually: 1. Stochastic programming (4 papers). 2. Subgradient theory (3 papers, 1 thesis). 3. Nonlinear programming (4 papers). 4. Optimal control (1 thesis). >_AIR IpORC' CE

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Deterministic and stochastic optimization problems of bolza type in discrete time

Cited by 33 publications

References 13 publications

Shadow price of information in discrete time stochastic optimization

Shadow price of information in discrete time stochastic optimization

Stochastic programming approaches to stochastic scheduling

Subgradient Methods in Deterministic and Stochastic Optimization.

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