Selecting the objective functional: conjugate duality

1983 ◽  
pp. 21-25
Author(s):  
Wray Britton
Keyword(s):  
Conjugate Duality ◽  
Objective Functional

Convexity of a discrete Carleman weighted objective functional in an inverse medium scattering problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Nguyen Trung Thành
Keyword(s):  
Finite Number ◽  
Scattering Problem ◽  
One Dimensional ◽  
Globally Convergent ◽  
Convergent Method ◽  
Inverse Medium ◽  
Inverse Medium Scattering ◽  
Objective Functional

AbstractWe investigate a globally convergent method for solving a one-dimensional inverse medium scattering problem using backscattering data at a finite number of frequencies. The proposed method is based on the minimization of a discrete Carleman weighted objective functional. The global convexity of this objective functional is proved.

NUMERICAL SOLUTION OF THE INVERSE PROBLEM FOR A SYSTEM OF DIFFERENTIAL EQUATIONS

2020 ◽  
pp. 106-110
Author(s):  
S.E. Kasenov ◽  
◽  
G.E. Kasenova ◽  
A.A. Sultangazin ◽  
B.D. Bakytbekova ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Differential Equations ◽  
Numerical Solution ◽  
Direct Problem ◽  
Nonlinear Differential Equations ◽  
Direct And Inverse Problems ◽  
Additional Information ◽  
Several Variables ◽  
Gradient Of The Functional ◽  
Objective Functional

The article considers direct and inverse problems of a system of nonlinear differential equations. Such problems are often found in various fields of science, especially in medicine, chemistry and economics. One of the main methods for solving nonlinear differential equations is the numerical method. The initial direct problem is solved by the Rune-Kutta method with second accuracy and graphs of the numerical solution are shown. The inverse problem of finding the coefficients of a system of nonlinear differential equations with additional information on solving the direct problem is posed. The numerical solution of this inverse problem is reduced to minimizing the objective functional. One of the methods that is applicable to nonsmooth and noisy functionals, unconditional optimization of the functional of several variables, which does not use the gradient of the functional, is the Nelder-Mead method. The article presents the NellerMead algorithm. And also a numerical solution of the inverse problem is shown.

Conjugate Duality in Facility Location

1995 ◽  
pp. 89-101 ◽  
Author(s):  
Carlton H. Scott ◽  
Thomas R. Jefferson ◽  
Soheila Jorjani
Keyword(s):  
Facility Location ◽  
Conjugate Duality

scholarly journals Model-Free, Occlusion Accommodating Active Contour Tracking

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Mohamed Ben Salah ◽  
Amar Mitiche
Keyword(s):  
Active Contour ◽  
Evolution Equations ◽  
Infrared Imaging ◽  
Contour Method ◽  
Image Modeling ◽  
Model Free ◽  
Level Set Evolution ◽  
Kernel Form ◽  
Objective Functional ◽  
Active Curve

This study investigates tracking in monocular image sequences by a model-free, occlusion accommodating active contour method. The objective functional contains a model-free shape tracking term to constrain the active curve in a frame to have a shape which approximates as closely as possible the shape of the active curve in the preceding frame. It complements a kernel photometric tracking term which constrains the active curve in a frame to enclose an intensity profile that matches as closely as possible the profile within the curve in the preceding frame. This data term is in kernel form so as to forgo image modeling. The method, which is exclusively driven by the curve/level set evolution equations derived from the objective functional Euler-Lagrange conditions, can track several objects independently. Experimental validation includes examples with infrared imaging, occlusion, clutter, and articulated motion.

scholarly journals Beurteilung funktioneller Einschränkungen bei degenerativen Erkrankungen der Lendenwirbelsäule: Wer hat Recht – der Arzt, der Patient oder der objektive Test?

Praxis ◽  
2017 ◽  
Vol 106 (19) ◽  
pp. 1041-1052 ◽  
Author(s):  
Martin N. Stienen ◽  
David Bellut ◽  
Luca Regli ◽  
Oliver N. Hausmann ◽  
Oliver P. Gautschi
Keyword(s):  
Functional Impairment ◽  
Timed Up And Go ◽  
Objective Functional Impairment ◽  
Objective Functional

Zusammenfassung. Zur exakten Erfassung von Schmerzen, funktionellen Einschränkungen und gesundheitsbezogener Lebensqualität bei Patienten mit degenerativen Wirbelsäulenerkrankungen existiert eine Reihe validierter Messinstrumente. Neben der Beurteilung durch den Therapeuten sowie «subjektiven» patientenorientierten Messmethoden (PROMs) wurde in den vergangenen Jahren der «Timed Up and Go»(TUG)-Test systematisch untersucht und als krankheitsspezifisches Messinstrument validiert. Heute kann eine objektive funktionelle Einschränkung (OFI = Objective Functional Impairment) in wenigen Sekunden und kostenfrei mithilfe einer Smartphone-Applikation bestimmt werden. Die Bestimmung von Z- oder T-Werten, die TUG-Testergebnisse in Relation zur Populationsnorm setzen, ermöglichen eine alters- und geschlechtsadjustierte Ergebnisinterpretation. Diese Übersichtsarbeit fasst die aktuellen Erkenntnisse zu objektiven Messmethoden bei degenerativen Wirbelsäulenpathologien inklusive deren Vor- und Nachteile zusammen und vergleicht sie mit den bisherigen Beurteilungsmethoden für funktionelle Outcomes.

scholarly journals Objective functional impairment in lumbar degenerative disease: concurrent validity of the baseline severity stratification for the five-repetition sit-to-stand test

2020 ◽  
Vol 33 (1) ◽  
pp. 4-11
Author(s):  
Anita M. Klukowska ◽  
Marc L. Schröder ◽  
Martin N. Stienen ◽  
Victor E. Staartjes
Keyword(s):  
Functional Impairment ◽  
Concurrent Validity ◽  
Leg Pain ◽  
Linear Regression Models ◽  
Lumbar Degenerative Disease ◽  
Baseline Severity ◽  
Sit To Stand ◽  
Patient Reported ◽  
Objective Functional Impairment ◽  
Objective Functional

OBJECTIVEThe five-repetition sit-to-stand (5R-STS) test provides a new dimension of clinical assessment by capturing objective functional impairment (OFI). Through the utilization of data from two prospective studies, the authors sought to evaluate the concurrent validity of the proposed 5R-STS baseline severity stratification (BSS) for OFI with the following levels based on time to completion in seconds: none, ≤ 10.4; mild, 10.5–15.2; moderate, 15.3–22.0; and severe, > 22.0 seconds.METHODSPatients with degenerative diseases of the spine performed the 5R-STS test and completed visual analog scales (VASs) for back and leg pain, the Oswestry Disability Index (ODI), the Roland-Morris Disability Questionnaire (RMDQ), and EQ-5D questionnaires. The degree of OFI severity was assessed based on the previously proposed BSS, and its association with patient-reported scales was evaluated using ANOVA as well as crude and adjusted linear regression models.RESULTSOur sample included 240 patients, of whom 101 exhibited no OFI, whereas 80, 34, and 25 were judged to have mild, moderate, and severe OFI, respectively. A higher baseline severity was strongly associated with loss of working ability (p < 0.001), as well as results of all patient-reported scales (p ≤ 0.001), with the exception of the VAS for leg pain (p = 0.556). Crude and adjusted regression analyses corroborated these findings, although only patients with moderate and severe OFI as judged by using the 5R-STS BSS demonstrated clinically relevant differences compared with patients without OFI.CONCLUSIONSThe degree of OFI—based on the 5R-STS BSS—is strongly associated with measures of back pain, subjective functional impairment, and health-related quality of life. However, leg pain severity is not reflected within the dimension of OFI measured by the 5R-STS. The proposed BSS appears to be a concurrently valid and clinically relevant measure of OFI in patients with degenerative spinal pathologies.

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