Necessary and sufficient conditions for weak efficiency in non-smooth vectorial optimization problems

Optimization ◽  
2009 ◽  
Vol 58 (8) ◽  
pp. 981-993 ◽  
Author(s):  
Lucelina Batista dos Santos ◽  
Adilson J.V. Brandão ◽  
Rafaela Osuna-Gómez ◽  
Marko A. Rojas-Medar
Keyword(s):  
Optimization Problems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weak Efficiency ◽  
Necessary And Sufficient

NECESSARY AND SUFFICIENT CONDITIONS FOR DYNAMIC OPTIMIZATION

2014 ◽  
Vol 20 (3) ◽  
pp. 667-684 ◽  
Author(s):  
A. Kerem Coşar ◽  
Edward J. Green
Keyword(s):  
Optimization Problems ◽  
Infinite Horizon ◽  
Sufficient Conditions ◽  
Transversality Condition ◽  
Necessary And Sufficient Conditions ◽  
Infinite Horizon Optimization ◽  
Sufficient Conditions For Optimality ◽  
The Government ◽  
Duality Approach ◽  
Necessary And Sufficient

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.

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

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.

scholarly journals Strong and Total Lagrange Dualities for Quasiconvex Programming

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
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.

scholarly journals Well-Posedness and Primal-Dual Analysis of Some Convex Separable Optimization Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Stefan M. Stefanov
Keyword(s):  
Computational Complexity ◽  
Optimization Problems ◽  
Saddle Points ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Well Posedness ◽  
Dual Analysis ◽  
Primal Dual ◽  
Necessary And Sufficient ◽  
Separable Optimization

We focus on some convex separable optimization problems, considered by the author in previous papers, for which problems, necessary and sufficient conditions or sufficient conditions have been proved, and convergent algorithms of polynomial computational complexity have been proposed for solving these problems. The concepts of well-posedness of optimization problems in the sense of Tychonov, Hadamard, and in a generalized sense, as well as calmness in the sense of Clarke, are discussed. It is shown that the convex separable optimization problems under consideration are calm in the sense of Clarke. The concept of stability of the set of saddle points of the Lagrangian in the sense of Gol'shtein is also discussed, and it is shown that this set is not stable for the “classical” Lagrangian. However, it turns out that despite this instability, due to the specificity of the approach, suggested by the author for solving problems under consideration, it is not necessary to use modified Lagrangians but only the “classical” Lagrangians. Also, a primal-dual analysis for problems under consideration in view of methods for solving them is presented.

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

2019 ◽  
Vol 74 (2) ◽  
pp. 233-253
Author(s):  
Washington Alves de Oliveira ◽  
Marko Antonio Rojas-Medar ◽  
Antonio Beato-Moreno ◽  
Maria Beatriz Hernández-Jiménez
Keyword(s):  
Optimization Problems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Optimal Solutions ◽  
Fractional Optimization ◽  
Global Optimal ◽  
Necessary And Sufficient

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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