scholarly journals Bilevel programs with extremal value function: global optimality

2005 ◽  
Vol 2005 (3) ◽  
pp. 419-435 ◽  
Author(s):  
Abdelmalek Aboussoror ◽  
Hicham Babahadda ◽  
Abdelatif Mansouri
Keyword(s):  
Value Function ◽  
Convex Set ◽  
Maximization Problem ◽  
Global Optimality ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Bilevel Program ◽  
Bilevel Programs ◽  
Necessary And Sufficient ◽  
Extremal Value

For a bilevel program with extremal value function, a necessary and sufficient condition for global optimality is given, which reduces the bilevel program to amax-minproblem with linked constraints. Also, for the case where the extremal value function is polyhedral, this optimality condition gives the possibility of a resolution via a maximization problem of a polyhedral convex function over a convex set. Finally, this case is completed by an algorithm.

EXISTENCE, UNIQUENESS, AND DETERMINACY OF A NONNEGATIVE EQUILIBRIUM PRICE VECTOR IN ASSET MARKETS WITH GENERAL UTILITY FUNCTIONS AND AN ELLIPTICAL DISTRIBUTION

2004 ◽  
Vol 21 (03) ◽  
pp. 393-405
Author(s):  
ZHIPING CHEN
Keyword(s):  
Equilibrium Price ◽  
Utility Functions ◽  
Equilibrium Analysis ◽  
Asset Market ◽  
Maximization Problem ◽  
Sufficient Condition ◽  
Elliptical Distribution ◽  
Necessary And Sufficient Condition ◽  
Price Vector ◽  
Necessary And Sufficient

For the asset market with finite numbers of investors whose utility functions are general concave functions, we derive a necessary and sufficient condition for the existence and uniqueness of the nonnegative equilibrium price vector that clears the asset market, through considering the expected utility maximization problem under the assumption that the joint distribution of risky assets' returns is an elliptical distribution. An explicit formula for the equilibrium price is given. We also discuss the economic implication of the given condition and demonstrate that our necessary and sufficient condition can be regarded as a necessary condition to maintain the stability of the asset market. These results extend some results about the equilibrium analysis of the asset market.

scholarly journals Proximinal subspaces ofA(K)of finite codimension

2003 ◽  
Vol 2003 (39) ◽  
pp. 2501-2505
Author(s):  
T. S. S. R. K. Rao
Keyword(s):  
Compact Subset ◽  
Convex Set ◽  
Compact Convex ◽  
Continuous Functions ◽  
Finite Codimension ◽  
Sufficient Condition ◽  
Choquet Simplex ◽  
Necessary And Sufficient Condition ◽  
Compact Convex Set ◽  
Necessary And Sufficient

We study an analogue of Garkavi's result on proximinal subspaces ofC(X)of finite codimension in the context of the spaceA(K)of affine continuous functions on a compact convex setK. We give an example to show that a simple-minded analogue of Garkavi's result fails for these spaces. WhenKis a metrizable Choquet simplex, we give a necessary and sufficient condition for a boundary measure to attain its norm onA(K). We also exhibit proximinal subspaces of finite codimension ofA(K)when the measures are supported on a compact subset of the extreme boundary.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

scholarly journals Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

Physics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 352-366
Author(s):  
Thomas Berry ◽  
Matt Visser
Keyword(s):  
Point Of View ◽  
Sufficient Condition ◽  
Use Of Self ◽  
Necessary And Sufficient Condition ◽  
Wigner Rotation ◽  
Inertial Frames ◽  
Explicit Formulae ◽  
Specific Implementation ◽  
Necessary And Sufficient ◽  
Lorentz Boosts

In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased in terms of the quaternion square root of the relative 4-velocity connecting the two inertial frames. Straightforward computations then lead to quite explicit and relatively simple algebraic formulae for the composition of 4-velocities and the Wigner angle. The Wigner rotation is subsequently related to the generic non-associativity of the composition of three 4-velocities, and a necessary and sufficient condition is developed for the associativity to hold. Finally, the authors relate the composition of 4-velocities to a specific implementation of the Baker–Campbell–Hausdorff theorem. As compared to ordinary 4×4 Lorentz transformations, the use of self-adjoint complexified quaternions leads, from a computational view, to storage savings and more rapid computations, and from a pedagogical view to to relatively simple and explicit formulae.

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