scholarly journals The role of duality in optimization problems involving entropy functionals with applications to information theory

1988 ◽  
Vol 58 (2) ◽  
pp. 209-223 ◽  
Author(s):  
A. Ben-Tal ◽  
M. Teboulle ◽  
A. Charnes
Keyword(s):  
Information Theory ◽  
Optimization Problems ◽  
Entropy Functionals ◽  
Duality In Optimization

The General Form of γ-Family of Quantum Relative Entropies

2011 ◽  
Vol 18 (02) ◽  
pp. 191-221
Author(s):  
Ryszard Paweł Kostecki
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Recent Result ◽  
Quantum Information Theory ◽  
Fenchel Duality ◽  
Commutative Case ◽  
Infinite Dimensional ◽  
Entropy Functionals ◽  
The Family

We use the Falcone–Takesaki non-commutative flow of weights and the resulting theory of non-commutative Lp spaces in order to define the family of relative entropy functionals that naturally generalise the quantum relative entropies of Jenčová–Ojima and classical relative entropies of Zhu–Rohwer, and belong to an intersection of families of Petz relative entropies with Bregman relative entropies. For the purpose of this task, we generalise the notion of Bregman entropy to the infinite-dimensional non-commutative case using the Legendre–Fenchel duality. In addition, we use the Falcone–Takesaki duality to extend the duality between coarse-grainings and Markov maps to the infinite-dimensional non-commutative case. Following the recent result of Amari for the Zhu–Rohwer entropies, we conjecture that the proposed family of relative entropies is uniquely characterised by the Markov monotonicity and the Legendre–Fenchel duality. The role of these results in the foundations and applications of quantum information theory is discussed.

On the role of pattern matching in information theory

1998 ◽  
Vol 44 (6) ◽  
pp. 2045-2056 ◽  
Author(s):  
A.D. Wyner ◽  
J. Ziv ◽  
A.J. Wyner
Keyword(s):  
Information Theory ◽  
Pattern Matching

scholarly journals MATHEMATICAL PROGRAMMING APPLICATIONS PECULIARITIES IN SHAKEDOWN PROBLEM/MATEMATINIO PROGRAMAVIMO TAIKYMO KONSTRUKCIJŲ PRISITAIKYMO UŽDAVINIUOSE YPATUMAI

2001 ◽  
Vol 7 (2) ◽  
pp. 106-114
Author(s):  
Ela Chraptovič ◽  
Juozas Atkočiūnas
Keyword(s):  
Mathematical Programming ◽  
Optimization Problems ◽  
Optimality Criteria ◽  
Point Of View ◽  
Design Matrix ◽  
Problem Solution ◽  
Strain Compatibility ◽  
Complete Set ◽  
Mechanical Interpretation

The theory of mathematical programming widely spread as a method of a solution of extreme problems. It accompanies the study of plastic theory problem from its posing up to final solution. However, here again from our point of view not all possibilities are realized. Unfortunately, the use of mathematical programming as an instrument of a numerical solution for structural analysis frequently is also restricted by that. The possibilities of mechanical interpretation of optimality criteria of applied algorithms are not uncovered. The global solution of the problem of mathematical programming exists, if Kuhn-Tucker conditions are satisfied. These conditions do not depend on the applied algorithm of a problem solution. The identity of Kuhn-Tucker conditions with a optimality criteria of Rosen algorithm is finding out in this research. The role of a design matrix for the creating of strain compatibility equations is clarified. The Kuhn-Tucker conditions mean the residual strain compatibility equations in analysis of elastic-plastic systems. It is proved in the article that for problems of limiting equilibrium the Kuhn-Tucker conditions include the dependences of the associated law of plastic flow. The Kuhn-Tucker conditions together with limitations of a source problem of account represent a complete set of dependences of the theory of shakedown. The correct mathematical and mechanical interpretation of the Kuhn-Tucker conditions allows to refuse a direct solution of a dual problem of mathematical programming. It makes easier the solution of optimization problems of structures at shakedown.

The Role of the Information Channel in Visual Computing

2020 ◽  
pp. 464-490
Author(s):  
Miquel Feixas ◽  
Mateu Sbert
Keyword(s):  
Information Theory ◽  
Communication Channel ◽  
Probability Distributions ◽  
Global Illumination ◽  
Three Dimensional ◽  
Information Channel ◽  
Visual Computing ◽  
The Social ◽  
Shared Information

Around seventy years ago, Claude Shannon, who was working at Bell Laboratories, introduced information theory with the main purpose of dealing with the communication channel between source and receiver. The communication channel, or information channel as it later became known, establishes the shared information between the source or input and the receiver or output, both of which are represented by random variables, that is, by probability distributions over their possible states. The generality and flexibility of the information channel concept can be robustly applied to numerous, different areas of science and technology, even the social sciences. In this chapter, we will present examples of its application to select the best viewpoints of an object, to segment an image, and to compute the global illumination of a three-dimensional virtual scene. We hope that our examples will illustrate how the practitioners of different disciplines can use it for the purpose of organizing and understanding the interplay of information between the corresponding source and receiver.

scholarly journals On Minimal Copulas under the Concordance Order

2019 ◽  
Vol 184 (3) ◽  
pp. 762-780 ◽  
Author(s):  
Jae Youn Ahn ◽  
Sebastian Fuchs
Keyword(s):  
Optimization Problems ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Negative Dependence ◽  
Kendall’S Tau ◽  
Kendall's Tau ◽  
Minimal Elements ◽  
Measures Of Concordance ◽  
Concordance Order

AbstractIn the present paper, we study extreme negative dependence focussing on the concordance order for copulas. With the absence of a least element for dimensions $$d\ge 3$$d≥3, the set of all minimal elements in the collection of all copulas turns out to be a natural and quite important extreme negative dependence concept. We investigate several sufficient conditions, and we provide a necessary condition for a copula to be minimal. The sufficient conditions are related to the extreme negative dependence concept of d-countermonotonicity and the necessary condition is related to the collection of all copulas minimizing multivariate Kendall’s tau. The concept of minimal copulas has already been proved to be useful in various continuous and concordance order preserving optimization problems including variance minimization and the detection of lower bounds for certain measures of concordance. We substantiate this key role of minimal copulas by showing that every continuous and concordance order preserving functional on copulas is minimized by some minimal copula, and, in the case the continuous functional is even strictly concordance order preserving, it is minimized by minimal copulas only. Applying the above results, we may conclude that every minimizer of Spearman’s rho is also a minimizer of Kendall’s tau.

Game and Information Theory in Modern Managerial Economics

2013 ◽  
pp. 128-154
Author(s):  
Esther Gal-Or
Keyword(s):  
Information Theory ◽  
Incomplete Information ◽  
Market Power ◽  
Entry Barriers ◽  
Market Failures ◽  
Short Term ◽  
Vertical Control ◽  
Managerial Economics

This chapter describes how methodologies developed in the field of game and information theory can assist in understanding the interaction of competitors in markets, and the study of managerial economics, in general. The chapter highlights, in particular, the role of incomplete information in generating market failures, and provides examples of mechanisms that can alleviate such failures. Some examples of topics addressed are: first- and second-mover advantages, long term strategic commitments versus short term tactical choices made by competitors, erection of entry barriers to secure market power, choices of product-mix, special pricing mechanisms to enhance profitability, and issues related to vertical control and the internal organization of the firm.

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