Extensions of Lagrange Multipliers in Nonlinear Programming

Gould, F. J.

doi:10.1137/0117120

Cited by 90 publications

(29 citation statements)

References 9 publications

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“…Thus, n can be thought of as the maximum number of additional degrees of freedom needed to price the output or the maximum additional dimensions needed for the space where the separating hyperplane or linear support function exists. In R m , the support function is nonconvex and poorly behaved (Gould 1971). In R m+n , there is always a separating hyperplane.…”

Section: Prices In the Lp That Solve The Mipmentioning

confidence: 99%

Efficient market-clearing prices in markets with nonconvexities

O’Neill

Sotkiewicz

Hobbs

et al. 2005

European Journal of Operational Research

340

222

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This paper addresses the existence of market clearing prices and the economic interpretation of strong duality for integer programs in the economic analysis of markets with nonconvexities (indivisibilities). Electric power markets in which nonconvexities arise from the operating characteristics of generators motivate our analysis; however, the results presented here are general and can be applied to other markets in which nonconvexities are important. We show that the optimal solution to a linear program that solves the mixed integer program has dual variables that: (1) have the traditional economic interpretation as prices; (2) explicitly price integral activities; and (3) clear the market in the presence of nonconvexities. We then show how this methodology can be used to interpret the solutions to nonconvex problems such as the problem discussed by Scarf (1994).Economics, Equilibrium Pricing; MIP models of markets, MIP Applications

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Section: Prices In the Lp That Solve The Mipmentioning

confidence: 99%

Efficient market-clearing prices in markets with nonconvexities

O’Neill

Sotkiewicz

Hobbs

et al. 2005

European Journal of Operational Research

340

222

View full text Add to dashboard Cite

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“…Cependant, cohérents avec eux-mêmes, 11. Par Arrow, Chenery, Hurwicz, Solow et Uzawa. les économistes se sont confinés au cas convexe et ont laissé aux mathématiciens, notamment à Gould (1969Gould ( , 1972, Rockafellar (1974), Tind et Wolsey (1981), le soin d'apporter les derniers raffinements à un théorie générale de la dualité.…”

Section: Programmation Non Linéaireunclassified

Programmation mathématique et théorie économique

Truchon

1988

L'Actualité économique

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“…According to the results by Huang and Shen [18], and its references such as Shannon [19], Skilling and Gull [20], Everett [21], Brooks and Geoffrion [22], Gould [23] and Greenberg and Pierskalla [24], Problem (5) is equivalent to the following problem: min z s.t.…”

Section: Maximum Entropy Methodsmentioning

confidence: 99%

A Maximum Entropy Method for a Robust Portfolio Problem

Zhu-wu

Jiang

et al. 2014

Entropy

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We propose a continuous maximum entropy method to investigate the robust optimal portfolio selection problem for the market with transaction costs and dividends. This robust model aims to maximize the worst-case portfolio return in the case that all of asset returns lie within some prescribed intervals. A numerical optimal solution to the problem is obtained by using a continuous maximum entropy method. Furthermore, some numerical experiments indicate that the robust model in this paper can result in better portfolio performance than a classical mean-variance model.

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Extensions of Lagrange Multipliers in Nonlinear Programming

Cited by 90 publications

References 9 publications

Efficient market-clearing prices in markets with nonconvexities

Efficient market-clearing prices in markets with nonconvexities

Programmation mathématique et théorie économique

A Maximum Entropy Method for a Robust Portfolio Problem

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