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
^The Boosted Difference of Convex Functions Algorithm for Nonsmooth Functionshttps://doi.org/10.1137/18M123339X
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 •...
We present a fast and robust nonconvex optimization approach for Fuzzy C-Means (FCM) clustering model. Our approach is based on DC (Difference of Convex functions) programming and DCA (DC Algorithms) that have been successfully applied in various fields of applied sciences, including Machine Learn...
Souza, J.C.O., Oliveira, P.R., Soubeyran, A.: Global convergence of a proximal linearized algorithm for difference of convex functions. Optim. Lett. 10(7), 1529–1539 (2016) Article MathSciNet Google Scholar Clarke, F.: Optimisation and nonsmooth analysis. Classics in applied mathematic...
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...
This paper studies the difference-of-convex (DC) penalty formulations and the associated difference-of-convex algorithm (DCA) for computing stationary solutions of linear programs with complementarity constraints (LPCCs). We focus on three such formulations and establish connections between their stationar...
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 ...
convex CPWL function as the pointwise-maximum over a set of affine functions, the DC CPWL representation enables the polytope regions defining a CPWL function to be implicitly defined by the affine functions making up the convex components. By searching the affine functions of the convex ...
Banach space W, R-+(p) and R-+(m) are respectively the nonnegative orthants of R-p and R-m, C is a nonempty closed convex subset of X, b is an element of W, and the functions f(i), g(i), h(j) and k(j) are convex for i = 1,..., p and j = 1, ldots, m. ...