Necessary and sufficient conditions for power convergence rate of approximations in Tikhonov’s scheme for solving ill-posed optimization problems

2017 ◽  
Vol 61 (6) ◽  
pp. 51-59 ◽  
Author(s):  
M. Yu. Kokurin
Keyword(s):  
Convergence Rate ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Tikhonov’S Scheme ◽  
Ill Posed ◽  
Necessary And Sufficient

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.

Influence of design on the rate of convergence to normality in L1 regression

1989 ◽  
Vol 106 (2) ◽  
pp. 355-368 ◽  
Author(s):  
Peter Hall ◽  
A. H. Welsh
Keyword(s):  
Convergence Rate ◽  
Rate Of Convergence ◽  
Edgeworth Expansion ◽  
Sufficient Conditions ◽  
Error Distribution ◽  
Necessary And Sufficient Conditions ◽  
Moment Condition ◽  
Regression Problem ◽  
Design Variables ◽  
Necessary And Sufficient

AbstractWe provide a concise account of the influence of design variables on the convergence rate in an L1 regression problem. In particular, we show that the convergence rate may be characterized precisely in terms of third and fourth moments of the design variables. This result leads to necessary and sufficient conditions on the design for the Berry-Esseen rate to be achieved. We also show that a moment condition on the error distribution is necessary and sufficient for a non-uniform Berry-Esseen theorem, and that an Edgeworth expansion is possible if the design points are not too clumped.

Sign in / Sign up

Export Citation Format

Share Document