We first develop an equivalent Difference of Convex functions (DC) representation for the non-convex Boolean constraint imposed on the association variables, making the problem tractable. Then, a DC algorithm is
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...
Due to the use of the ramp loss function, the corresponding objective function is nonconvex, making it more challenging. To overcome this limitation, we formulate our distance metric learning problem as an instance of difference of convex functions (DC) programming. This allows us to design a ...
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...
An approach to supervised distance metric learning based on difference of convex functions programming - bacnguyencong/DML-dc
We offer an efficient approach based on difference of convex functions (DC) optimization for self-organizing maps (SOM). We consider SOM as an optimization problem with a nonsmooth, nonconvex energy function and investigated DC programming and DC algorithm (DCA), an innovative approach in nonconve...
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 ...
In this paper, we study optimality conditions for vector optimization problems of a difference of convex mappings (VP) {R-+(p)- - Minimize f (x)- g(x), subject to the constraints x is an element of C, l(x)is an element of- Q, Ax = b and h(x)- k(x) is an element of-...
Difference constraints have been used for termination analysis in the literature, where they denote relational inequalities of the form $$x' \le y + c$
Keywords:Criticalpoint,d.c.Functions,Differenceofconvexfunctions,Generalizedderivatives, Minimization,Optimalityconditions,Palais-Smalecondition,Subdifferentials. 1.Introduction Thereisanabundanceofproblemswhichinvolvedifferencefunctions.Wecalla function:onanormedvectorspace(n.v.s.)adifferencefunctionifit ...