Given a nonconvex function f defined as the difference of two convex functions g and h (f is a so-called d.c. function), we study the regularized (or smoothed) version of f obtained by performing the infimal co
function J 2m (T,V) is concave in variable T (since H(T,V ) is convex). Hence S (sphere, i.e., boundary) contains minimizers (reaching at boundary) of J 2m (T,V ) on B, i.e., DC Formulation where Solving FCM by DCA (1) A key: construct two sequences (Y l , Z ...
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 ...
今天介绍的这种算法,Difference of Convex Algorithm,也就是DCA,以便咱们解决非凸优化问题。 但这种问题仅仅针对某些特定情况。 首先,咱们对这串英文进行解读,Difference理解为差,convex是凸,即凸函数,algorithm嘛,你们自己查词典,哈哈哈。所以呢,DCA就是两个凸函数的差的算法。 你们肯定懵逼了,啥凸函数的差?Emmm, ...
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...
1992: New types of variational principles based on the notion of quasidifferentiability.Acta Mech. 94, 171–194 Polyakova, L.N. 1986: On minimizing the sum of a convex function and a concave function.Math. Prog. Study 19, 69–73 Rozvany, G.I.N. 1970: Concave programming in ...
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 ...
Difference-of-convex piecewise linear representation Definition 2 A real-valued functionfon a convex setC⊆Rnis called DC onCif there are two convex functionsf+,f−:C→Rsuch that:f(x)=f+(x)−f−(x)∀x∈C, The functionfis called a DC function iffis DC onRn. The representation...
Paper tables with annotated results for Further properties of the forward-backward envelope with applications to difference-of-convex programming
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...