Introduction to duality in optimization theory

1996 ◽  
Vol 91 (3) ◽  
pp. 523-542 ◽  
Author(s):  
J. Brinkhuis
Keyword(s):  
Optimization Theory ◽  
Duality In Optimization

scholarly journals Dual S-matrix bootstrap. Part I. 2D theory

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Andrea L. Guerrieri ◽  
Alexandre Homrich ◽  
Pedro Vieira
Keyword(s):  
Optimization Theory ◽  
Scattering Matrix ◽  
Dual Approach ◽  
Physical Systems ◽  
Crossing Symmetry ◽  
S Matrix ◽  
Primal Formulation ◽  
Rigorous Bounds ◽  
Duality In Optimization ◽  
Stable Particles

Abstract Using duality in optimization theory we formulate a dual approach to the S-matrix bootstrap that provides rigorous bounds to 2D QFT observables as a consequence of unitarity, crossing symmetry and analyticity of the scattering matrix. We then explain how to optimize such bounds numerically, and prove that they provide the same bounds obtained from the usual primal formulation of the S-matrix Bootstrap, at least once convergence is attained from both perspectives. These techniques are then applied to the study of a gapped system with two stable particles of different masses, which serves as a toy model for bootstrapping popular physical systems.

A Study on the Contour of the Radial Tire: Rolling Contour Optimization Theory — RCOT

1987 ◽  
Vol 15 (1) ◽  
pp. 3-29 ◽  
Author(s):  
K. Yamagishi ◽  
M. Togashi ◽  
S. Furuya ◽  
K. Tsukahara ◽  
N. Yoshimura
Keyword(s):  
Fuel Efficiency ◽  
Optimization Theory ◽  
Radial Tire ◽  
Braking Performance ◽  
Equilibrium Profiles ◽  
Natural Equilibrium

Abstract The Rolling Contour Optimization Theory (RCOT) can lead to improved steering, fuel efficiency, riding comfort, and braking performance of tires relative to those of conventional shape. The conventional shape has been guided by natural equilibrium profiles, while the RCOT technology shape is guided by that of the tire in motion. This reduces useless distortions caused by running the tire under load. The RCOT design focuses on the distribution of belt and sidewall tension in the tire. Controlling tension in the belt and carcass area while the tire is in motion was the key to creating this new tire shape.

Making the Most of the Internet for Failure Analysis

1998 ◽  
Author(s):  
Dan J. Bodoh
Keyword(s):  
New Media ◽  
Failure Analysis ◽  
Digital Media ◽  
Optimization Theory ◽  
The Internet ◽  
Digital Medium ◽  
Production Distribution ◽  
Digital Production ◽  
Computer Monitors ◽  
And Storage

Abstract The growth of the Internet over the past four years provides the failure analyst with a new media for communicating his results. The new digital media offers significant advantages over analog publication of results. Digital production, distribution and storage of failure analysis results reduces copying costs and paper storage, and enhances the ability to search through old analyses. When published digitally, results reach the customer within minutes of finishing the report. Furthermore, images on the computer screen can be of significantly higher quality than images reproduced on paper. The advantages of the digital medium come at a price, however. Research has shown that employees can become less productive when replacing their analog methodologies with digital methodologies. Today's feature-filled software encourages "futzing," one cause of the productivity reduction. In addition, the quality of the images and ability to search the text can be compromised if the software or the analyst does not understand this digital medium. This paper describes a system that offers complete digital production, distribution and storage of failure analysis reports on the Internet. By design, this system reduces the futzing factor, enhances the ability to search the reports, and optimizes images for display on computer monitors. Because photographic images are so important to failure analysis, some digital image optimization theory is reviewed.

Optimization Theory with Applications.

1970 ◽  
Vol 21 (3) ◽  
pp. 379
Author(s):  
K. B. Haley ◽  
Donald A. Pierre
Keyword(s):  
Optimization Theory

The Application of Fuzzy Optimization Theory in the Selection of Foundation Improvement Methods

2015 ◽  
Vol 723 ◽  
pp. 341-344
Author(s):  
Li Juan Zhang ◽  
Jiang Han ◽  
Zhang Ming Li
Keyword(s):  
Evaluation Criteria ◽  
Fuzzy Optimization ◽  
Optimization Theory ◽  
Static Method ◽  
Optimal Selection ◽  
Construction Time ◽  
Optimal Degree ◽  
Selection Of

Research was conducted on the optimal selection of foundation improvement methods in the paper. Based on fuzzy optimization theory, four evaluation criteria such as construction time are used to evaluate the five improvement methods. The relative optimal degree 0.798 of dynamic-static consolidation method is the maximum which shows that the dynamic-static method is the optimal one; relative optimal degree and multi-evaluating criteria are used to evaluate multi-goals in the fuzzy optimization theory which will lead to the high optimal reliability result.

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