DC programmingNonsmooth optimizationVariational analysisOptimization methods for difference-of-convex programs iteratively solve convex subproblems to define iterates. Although convex, depending on the problem's structure, these subproblems are very often challenging and require specialized solvers. This work ...
de Oliveira, W., Tcheou, M.P.: An inertial algorithm for DC programming. Set-Valued Var. Anal. 27(4), 895–919 (2019) Article MathSciNet Google Scholar Tuy, H.: Convex Analysis and Global Optimization, Nonconvex Optimization and Its Applications, vol. 22. Springer, Berlin (2016) Bo...
FunctionsandDCProgramming SongcanChen Outline 1.ABriefHistory 2.DCFunctionsandtheirProperty 3.Someexamples 4.DCProgramming 5.CaseStudy 6.Ournextwork 1.ABriefHistory •1964,HoangTuy,(incidentallyinhisconvex optimizationpaper), •1979,J.F.Toland,Dualityformulation •1985,PhamDinhTao,DCAlgorithm •...
Paper tables with annotated results for Further properties of the forward-backward envelope with applications to difference-of-convex programming
DC programmingDistance metric learning has motivated a great deal of research over the last years due to its robustness for many pattern recognition problems. In this paper, we develop a supervised distance metric learning method that aims to improve the performance of nearest-neighbor classification....
Such a formulation has been modified by Kong and Maravelias (2020) and Rebennack and Krasko (2020) to transform it into a MILP (or mixed integer quadratic programming, MIQP) problem. Several modeling frameworks, such as hinging hyperplane and difference of convex, have been also incorporated...
An approach to supervised distance metric learning based on difference of convex functions programming - bacnguyencong/DML-dc
X⇒ZareZ+-convexsetvaluedmappings.688N.GADHISuchaproblemhasbeendiscussedbyseveralauthorsatvariouslevelsofgenerality[3–6,8–10,15,18,19].Initsframework,(P)includesmanyotherproblems,likeconvexset-valuedoptimizationproblems,vectoroptimizationproblems,mathematicalprogrammingproblems,etc.Ourapproachconsistsofusing...
We develop advanced DCAs (Difference of Convex functions Algorithms) for these problems, which are based on DC Programming and DCA – the powerful tools for non-smooth non-convex optimization problems. Firstly, we consider the problem of group variable selection in multi-class logistic regression....
Also an application to vector fractional mathematical programming is given. Our contribution extends the results obtained in scalar optimization by Hiriart-Urruty [ 9] and improve substantially the few results known in vector case ( see for instance: [ 11], [ 12] and [ 14]). 展开 ...