Necessary and sufficient conditions for achieving global optimal solutions in multiobjective quadratic fractional optimization problems

We characterize the necessary and sufficient conditions for optimality in discrete-time, infinite-horizon optimization problems with a state space of finite or infinite dimension. It is well known that the challenging task in this problem is to prove the necessity of the transversality condition. To do this, we follow a duality approach in an abstract linear space. Our proof resembles that of Kamihigashi (2003), but does not explicitly use results from real analysis. As an application, we formalize Sims's argument that the no-Ponzi constraint on the government budget follows from the necessity of the tranversality condition for optimal consumption.

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Necessary and sufficient conditions for optimal solutions to a survivor search problem

Mathematical Programming Studies - Stochastic Systems: Modeling, Identification and Optimization, II ◽

10.1007/bfb0120754 ◽

1976 ◽

pp. 227-245 ◽

Cited By ~ 4

Author(s):

Lawrence D. Stone

Keyword(s):

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Search Problem ◽

Optimal Solutions ◽

Necessary And Sufficient

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Preservation of Supermodularity in Parametric Optimization: Necessary and Sufficient Conditions on Constraint Structures

Operations Research ◽

10.1287/opre.2020.1992 ◽

2020 ◽

Author(s):

Xin Chen ◽

Daniel Zhuoyu Long ◽

Jin Qi

Keyword(s):

Operations Research ◽

Parametric Optimization ◽

Optimization Problems ◽

Lattice Structure ◽

Sufficient Conditions ◽

Comparative Statics ◽

Necessary And Sufficient Conditions ◽

Objective Functions ◽

New Concepts ◽

Necessary And Sufficient

The concept of supermodularity has received considerable attention in economics and operations research. It is closely related to the concept of complementarity in economics and has also proved to be an important tool for deriving monotonic comparative statics in parametric optimization problems and game theory models. However, only certain sufficient conditions (e.g., lattice structure) are identified in the literature to preserve the supermodularity. In this article, new concepts of mostly sublattice and additive mostly sublattice are introduced. With these new concepts, necessary and sufficient conditions for the constraint structures are established so that supermodularity can be preserved under various assumptions about the objective functions. Furthermore, some classes of polyhedral sets that satisfy these concepts are identified, and the results are applied to assemble-to-order systems.

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Optimality Conditions for Pareto-Optimal Solutions

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.685.142 ◽

2016 ◽

Vol 685 ◽

pp. 142-147

Author(s):

Vladimir Gorbunov ◽

Elena Sinyukova

Keyword(s):

Multicriteria Optimization ◽

Optimization Problem ◽

Necessary Conditions ◽

Optimization Problems ◽

Linear Optimization ◽

Sufficient Conditions ◽

Optimal Solutions ◽

Main Criterion ◽

Linear Optimization Problems ◽

Necessary And Sufficient

In this paper the authors describe necessary conditions of optimality for continuous multicriteria optimization problems. It is proved that the existence of effective solutions requires that the gradients of individual criteria were linearly dependent. The set of solutions is given by system of equations. It is shown that for finding necessary and sufficient conditions for multicriteria optimization problems, it is necessary to switch to the single-criterion optimization problem with the objective function, which is the convolution of individual criteria. These results are consistent with non-linear optimization problems with equality constraints. An example can be the study of optimal solutions obtained by the method of the main criterion for Pareto optimality.

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Optimization Problems on Extremal Algebras: Necessary and Sufficient Conditions for Optimal Points

International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique - Parametric Optimization and Approximation ◽

10.1007/978-3-0348-6253-0_11 ◽

1984 ◽

pp. 166-184

Author(s):

Siegfried Helbig

Keyword(s):

Optimization Problems ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Necessary And Sufficient

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Strong and Total Lagrange Dualities for Quasiconvex Programming

Journal of Applied Mathematics ◽

10.1155/2014/453912 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8 ◽

Cited By ~ 6

Author(s):

Donghui Fang ◽

XianFa Luo ◽

Xianyun Wang

Keyword(s):

Optimization Problems ◽

Constraint Qualifications ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Quasiconvex Programming ◽

Quasiconvex Optimization ◽

Necessary And Sufficient

We consider the strong and total Lagrange dualities for infinite quasiconvex optimization problems. By using the epigraphs of thez-quasi-conjugates and the Greenberg-Pierskalla subdifferential of these functions, we introduce some new constraint qualifications. Under the new constraint qualifications, we provide some necessary and sufficient conditions for infinite quasiconvex optimization problems to have the strong and total Lagrange dualities.

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