difference of two convex functionsouter approximation methodgeneralized Benders’ decompositionconcave minimizationindefinite quadratic programmingWe study the problem of finding the global minimum of the difference between two convex functions f(x)−g(y) , under linear constraints of the form: x∈X, ...
Quasiconvex functionDifference of quasiconvex functionsQ-subdifferentialOptimality conditionsIn this note, we are concerned with an optimization problem (P) where the objective function is the difference of two quasiconvex functions. Using a suitable subdifferential introduced by Suzuki and Kuroiwa (...
D. Melzer: 1986, ‘On the expressibility of piecewise-linear continuous functionsss as the difference of two piecewise-linear convex functions,’Mathematical Programming Study 29 , 118-134.Melzer, D. (1986). On the expressibility of piecewise- linear continuous functions as a difference of two ...
DifferenceOfConvex(DC) 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,Pham...
Two new penalty methods for sparse reconstruction are proposed based on two types of difference of convex functions (DC for short) programming in which the DC objective functions are the difference of l1 and lσ q norms and the difference of l1 and lr norms with r > 1. By introducing a ...
We improve this result by constructing a delta convex function of class $C^1(\Bbb R^2)$ which cannot be represented as a difference of two convex functions differentiable at 0. Further we give an example of a delta convex function differentiable everywhere which is not strictly differentiable...
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We show that the class of all delta-convex selfmappings of R (differences of two convex functions) enjoys the difference property in the sense of N.G. de Bruijn. The Q-differentiability technique has been applied as a proof tool. (C) 2013 Royal Dutch Mathematical Society (KWG). Published...
Keywords:Criticalpoint,d.c.Functions,Differenceofconvexfunctions,Generalizedderivatives, Minimization,Optimalityconditions,Palais-Smalecondition,Subdifferentials. 1.Introduction Thereisanabundanceofproblemswhichinvolvedifferencefunctions.Wecalla function:onanormedvectorspace(n.v.s.)adifferencefunctionifit ...
An approach to supervised distance metric learning based on difference of convex functions programming - bacnguyencong/DML-dc