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Benson type algorithms for linear vector optimization and applications

Hamel, Andreas; Löhne, Andreas; Rudloff, Birgit - In: Journal of Global Optimization 59 (2014) 4, pp. 811-836

New versions and extensions of Benson’s outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each iteration rather than two or three as in previous...

Persistent link: https://www.econbiz.de/10010994156

Farkas’ lemma: three decades of generalizations for mathematical optimization

Dinh, N.; Jeyakumar, V. - In: TOP: An Official Journal of the Spanish Society of … 22 (2014) 1, pp. 1-22

In this paper we present a survey of generalizations of the celebrated Farkas’s lemma, starting from systems of linear inequalities to a broad variety of non-linear systems. We focus on the generalizations which are targeted towards applications in continuous optimization. We also briefly...

Persistent link: https://www.econbiz.de/10010995373

On the game interpretation of a shadow price process in utility maximization problems under transaction costs

Rokhlin, Dmitry - In: Finance and Stochastics 17 (2013) 4, pp. 819-838

interpretation of shadow prices via Lagrange duality. Copyright Springer-Verlag Berlin Heidelberg 2013 …

Persistent link: https://www.econbiz.de/10010997073

Dual methods for probabilistic optimization problems<Superscript>*</Superscript>

Dentcheva, Darinka; Lai, Bogumila; Ruszczyński, Andrzej - In: Mathematical Methods of Operations Research 60 (2004) 2, pp. 331-346

We consider nonlinear stochastic optimization problems with probabilistic constraints. The concept of a p-efficient point of a probability distribution is used to derive equivalent problem formulations, and necessary and sufficient optimality conditions. We analyze the dual functional and its...

Persistent link: https://www.econbiz.de/10010999538

A duality approach to problems of combined stopping and deciding under constraints

Balzer, Thomas; Janßen, Klaus - In: Mathematical Methods of Operations Research 55 (2002) 3, pp. 431-446

to show that there is no duality gap between the primal constrained optimization problem and the dual problem involving …

Persistent link: https://www.econbiz.de/10010999654

Set-valued duality theory for multiple objective linear programs and application to mathematical finance

Heyde, Frank; Löhne, Andreas; Tammer, Christiane - In: Mathematical Methods of Operations Research 69 (2009) 1, pp. 159-179

We develop a duality theory for weakly minimal points of multiple objective linear programs which has several … are hyperplanes. As in other set-valued (but not in vector-valued) approaches, there is no duality gap in the case that … in a complete lattice. Thus the duality theory has a high degree of analogy to its classical counterpart. Another …

Persistent link: https://www.econbiz.de/10010999730

Increasing quasiconcave co-radiant functions with applications in mathematical economics

Martínez-Legaz, Juan Enrique; Rubinov, Alexander M.; … - In: Mathematical Methods of Operations Research 61 (2005) 2, pp. 261-280

coradiant quasiconcave increasing functions. We use this generator to examine two duality schemes for these functions: classical … duality often used in microeconomic analysis and a more recent duality concept. Some possible applications to the theory of …

Persistent link: https://www.econbiz.de/10010999761

Duality of welfare and profit maximization

Boccard, Nicolas - In: Economics Letters 113 (2011) 3, pp. 215-217

duality existing between the welfarist and monopolist constrained maximization programs by proving the following “folk theorem …

Persistent link: https://www.econbiz.de/10011041827

Benefit-of-the-doubt aggregation and the diet problem

Färe, Rolf; Karagiannis, Giannis - In: Omega 47 (2014) C, pp. 33-35

In this note we show that the diet problem and the benefit-of-the-doubt (BoD) aggregation are linear programming duals. That is, the primal (dual) formulation of the diet problem is equivalent to the dual (primal) formulation of the BoD model as long as food prices are set equal to one. In...

Persistent link: https://www.econbiz.de/10011051804

A unifying framework for duality and modeling in robust linear programs

Soyster, A.L.; Murphy, F.H. - In: Omega 41 (2013) 6, pp. 984-997

In this paper, our major theme is a unifying framework for duality in robust linear programming. We show that there are …

Persistent link: https://www.econbiz.de/10011051853