Sufficient conditions and perfect duality in nonconvex minimization with inequality constraints

Simple item page
dc.contributorVirginia Techen
dc.contributor.authorGao, D. Y.en
dc.contributor.departmentMathematicsen
dc.date.accessed2014-05-09en
dc.date.accessioned2014-05-14T13:23:41Zen
dc.date.available2014-05-14T13:23:41Zen
dc.date.issued2005-02en
dc.description.abstractThe paper studies forced surface waves on an incompressible, inviscid fluid in a two-dimensional channel with a small negative or oscillatory bump on a rigid flat bottom. Such wave motions are determined by a non-dimensional wave speed F, called Froude number, and F = 1 is a critical value of F. If F = 1 + lambda epsilon with a small parameter epsilon > 0, then a forced Korteweg-deVries (FKdV) equation can be derived to model the wave motion on the free surface. In this paper, the case lambda > 0 (or F > 1, called supercritical case) is considered. The steady and unsteady solutions of the FKdV equation with a negative bump function independent of time are first studied both theoretically and numerically. It is shown that there are five steady solutions and only one of them, which exists for all lambda > 0, is stable. Then, solutions of the FKdV equation with an oscillatory bump function posed on R or a finite interval are considered. The corresponding linear problems are solved explicitly and the solutions are rigorously shown to be eventually periodic as time goes to infinity, while a similar result holds for the nonlinear problem posed on a finite interval with small initial data and forcing functions. The nonlinear solutions with zero initial data for any forcing functions in the real line R or large forcing functions in a finite interval are obtained numerically. It is shown numerically that the solutions will become eventually periodic in time for a small forcing function. The behavior of the solutions becomes quite irregular as time goes to infinity, if the forcing function is large.en
dc.identifier.citationGao, D. Y., "Sufficient conditions and perfect duality in nonconvex minimization with inequality constraints," J. Industrial and Management Optimization 1(1), 53-63, (2005); DOI: 10.3934/dcdsb.2010.14.1313en
dc.identifier.doihttps://doi.org/10.3934/dcdsb.2010.14.1313en
dc.identifier.issn1547-5816en
dc.identifier.urihttp://hdl.handle.net/10919/47979en
dc.identifier.urlhttps://www.aimsciences.org/journals/displayArticles.jsp?paperID=869en
dc.language.isoen_USen
dc.publisherAmerican Institute of Mathematical Sciencesen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectforced surface wavesen
dc.subjectnegative forcingen
dc.subjectoscillatory forcingen
dc.subjectde-vries equationen
dc.subjectforced-oscillationsen
dc.subjectmoving disturbancesen
dc.subjectmodelen
dc.subjectequationen
dc.subjectsolitary wavesen
dc.subjectquarter planeen
dc.subjectgravity-wavesen
dc.subjectkdv equationen
dc.subjectwater-wavesen
dc.subjectflowen
dc.subjectmathematics, applieden
dc.titleSufficient conditions and perfect duality in nonconvex minimization with inequality constraintsen
dc.title.serialJournal of Industrial and Management Optimizationen
dc.typeArticle - Refereeden

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
nonconvex.pdf
Size:
226.86 KB
Format:
Adobe Portable Document Format
Description:
Main article
Download

Collections

Scholarly Works, Mathematics