Duality Analysis Research Articles

No title] - Linear and integer programming theory and practice, by Gerard Sierksma. $175. 1996. ISBN 0 8247 9695 0 (Marcel Dekker).

Linear optimisation basic concepts Dantzig's simplex method duality and optimality sensitivity analysis karmarkar's interior path method integer linear optimisation linear network models computational complexity issues model building, case studies, and advanced techniques solutions to selected exercises. Appendices: linear algebra convexity graph theory optimisation theory computer package INTPM.

Why German Schon and Noch are Still Duals: a Reply to van der Auwera

The paper takes up the objections raised in van der Auwera (1993) against the joint analysis of the German particles schon, noch and erst published in Lobner (1989). Central to my analysis is the claim that the particles are organized in duality groups of four to which essentially the same type of analysis applies. Van der Auwera (1993) claims that already/schon, in its basic use, is different from the other three particles in having a more complex meaning which results in an opposition of the particle to finally/endlich. As to the narrow-focus temporal uses he argues that the duality approach is inadequate in including improper members on the one hand, and excluding relevant particles on the other. The criticism will be refuted. After a recollection of the duality analysis in Section 2, van der Auwera's arguments against the general design of my analysis are dealt with in Section 3. It will be argued that his own analysis of already/schon and its group, as far as it is supported by the data, does not really differ from my approach. In Section 4, I will deal with the claim that finally/endlich contradicts already/schon, which if correct would provide an indirect argument against the duality analysis of schon and noch. I will argue that endlich is set apart from the particles of the schon group by the presence of a non-descriptive, expressive, meaning component. For its descriptive meaning, endlich logically entails schon and belongs to a parallel duality group of its own together with noch immer. The apparent incompatibility of finally/endlich and already/schon can be explained as a conflict between what is foregrounded by each particle, respectively. In Section 5, I will argue that, contrary to van der Auwera's claims, the narrow focus uses of schon and its kin do form proper duality groups. The existence of such uses of noch, not treated in Lobner (1989), does not invalidate the duality analysis of schon and erst. Rather, noch in its relevant narrow-focus use belongs to yet another duality group together with its dual nur noch.

Exclusive QCD processes, quark-hadron duality, and the transition to perturbative QCD

Experiments at CEBAF will scan the intermediate-energy region of the QCD dynamics for the nucleon form factors and for Compton Scattering. These experiments will definitely clarify the role of resummed perturbation theory and of quark-hadron duality (QCD sum rules) in this regime. With this perspective in mind, we review the factorization theorem of perturbative QCD for exclusive processes at intermediate energy scales, which embodies the transverse degrees of freedom of a parton and the Sudakov resummation of the corresponding large logarithms. We concentrate on the pion and proton electromagnetic form factors and on pion Compton scattering. New ingredients, such as the evolution of the pion wave function and the complete two-loop expression of the Sudakov factor, are included. The sensitivity of our predictions to the infrared cutoff for the Sudakov evolution is discussed. We also elaborate on QCD sum rule methods for Compton Scattering, which provide an alternative description of this process. We show that, by comparing the local duality analysis to resummed perturbation theory, it is possible to describe the transition of exclusive processes to perturbative QCD.

Barycentric scenario trees in convex multistage stochastic programming

This work deals with the approximation of convex stochastic multistage programs allowing prices and demand to be stochastic with compact support. Based on earlier results, sequences of barycentric scenario trees with associated probability trees are derived for minorizing and majorizing the given problem. Error bounds for the optimal policies of the approximate problem and duality analysis with respect to the stochastic data determine the scenarios which improve the approximation. Convergence of the approximate solutions is proven under the stated assumptions. Preliminary computational results are outlined.

Duality theorems for convex problems with time delay

In this paper, we examine a class of convex problems of Bolza type, involving a time delay in the state. It encompasses a variety of time-delay problems arising in the calculus of variations and optimal control. A duality analysis is carried out which, among other things, leads to a characterization of minimizers in terms of the Euler-Lagrange inclusion. The results obtained improve in significant respects on what is achievable by techniques previously employed, based on elimination of the time delay by introduction of an infinite-dimensional state space or on the method of steps.

A duality analysis on stochastic partial differential equations

The duality equations of stochastic partial differential equations are solved in the Sobolev space H m (= W 2 m ( R d )), and the H m -norm estimates of the solutions are obtained. As an application, the H m -norm estimates with negative m for the solutions of stochastic partial differential equations are derived.

A DIAGRAMMATIC APPROACH FOR TEACHING SOME ASPECTS OF PRODUCTION‐COST DUALITY

Production‐cost duality was first introduced by Ronald Shephard (1953) in his seminal study, Cost and Production Functions. The application of duality to production and cost was extended by Uzawa (1962, 1964). However, not until the 1970s did the Shephard‐Uzawa duality analysis achieve its influential role in modern microeconomic thought. In simple words, the Shephard‐Uzawa duality theorem indicates that a firm's cost function summarizes all of the relevant features of the production technology, whereas the firm's production function contains all of the relevant features of the cost function for each set of input and output prices. If certain standard technical conditions (i.e., relating to convexity and continuity) are satisfied, then the theorem implies that there is a one‐to‐one relationship between points on the cost surface and points on the production surfaces.

QCD duality analysis of the kaon-to-vacuum weak matrix element.

We study the kaon-to-vacuum weak matrix element using the method of QCD sum rules. Both perturbative and nonperturbative contributions to the relevant Green's function are computed. It is found that the matrix element in question can be expressed as a sum of two terms: one behaving like {ital m}{sub {ital s}}{minus}m{sub {ital d}} and the other like {l angle}{ital {bar d}d}{r angle}{minus}{l angle}{ital {bar s}s}{r angle}. Numerical evaluations are also given.

QCD duality analysis of [formula omitted] mixing

Using finite energy sum rules, the hadronic matrix element of the ΔB=2 operator governing the mixing between the B 0 and B 0 mesons is evaluated. The result is very sensitive to the input value of the bottom quark mass. Allowing it to vary in the range m b =4.70±0.14 GeV, one finds ξ B |ƒ B | |B B | =0.13±0.05 GeV .

Duality, Indifference and Sensitivity Analysis in Multiple Objective Linear Programming

Duality, Indifference and Sensitivity Analysis in Multiple Objective Linear Programming

Duality, Indifference and Sensitivity Analysis in Multiple Objective Linear Programming — A Reply

Duality, Indifference and Sensitivity Analysis in Multiple Objective Linear Programming — A Reply

Duality, Indifference and Sensitivity Analysis in Multiple Objective Linear Programming -- A Reply

Duality, Indifference and Sensitivity Analysis in Multiple Objective Linear Programming -- A Reply

Duality, Indifference and Sensitivity Analysis in Multiple Objective Linear Programming

Duality, Indifference and Sensitivity Analysis in Multiple Objective Linear Programming

Duality, Indifference and Sensitivity Analysis in Multiple Objective Linear Programming

Duality, Indifference and Sensitivity Analysis in Multiple Objective Linear Programming

A duality analysis of the transportation problem

A duality analysis of the transportation problem

Duality and harmonic analysis on central topological groups. II

Duality and harmonic analysis on central topological groups. II

Duality and harmonic analysis on central topological groups. I

Duality and harmonic analysis on central topological groups. I

Correction to duality and harmonic analysis on central topological groups

Correction to duality and harmonic analysis on central topological groups

Duality and transportation analysis

Duality and transportation analysis

Duality and transportation analysis

Duality and transportation analysis