New Proximal Bundle Method for Non- smooth DC Optimization
نویسندگان
چکیده
In this paper, we develop a version of the bundle method to locally solve unconstrained difference of convex (DC) programming problems. It is assumed that a DC representation of the objective function is available. Our main idea is to use subgradients of both the first and second components in the DC representation. This subgradient information is gathered from some neighborhood of the current iteration point and it is used to build separately an approximation for each component in the DC representation. By combining these approximations we obtain the so-called nonconvex cutting plane model of the original objective function. We design the proximal bundle method for DC programming based on this approach and prove the convergence of the method to an ε-critical point. This algorithm is tested using some academic test problems.
منابع مشابه
Double Bundle Method for Nonsmooth DC Optimization
The aim of this paper is to introduce a new proximal double bundle method for unconstrained nonsmooth DC optimization, where the objective function is presented as a difference of two convex (DC) functions. The novelty in our method is a new stopping procedure guaranteeing Clarke stationarity for solutions by utilizing only DC components of the objective function. This optimality condition is s...
متن کاملA Doubly Inexact Interior Proximal Bundle Method for Convex Optimization
We propose a version of bundle method for minimizing a non-smooth convex function. Our bundle method have three features. In bundle method, we approximate the objective with some cutting planes and minimize the model with some stabilizing term. Firstly, it allows inexactness in this minimization. At the same time, evaluations of the objective and the subgradient are also required to generate th...
متن کاملBundle-type methods uniformly optimal for smooth and nonsmooth convex optimization
The bundle-level method and its certain variants are known to exhibit an optimal rate of convergence, i.e., O(1/ √ t), and also excellent practical performance for solving general non-smooth convex programming (CP) problems. However, this rate of convergence is significantly worse than the optimal one for solving smooth CP problems, i.e., O(1/t). In this paper, we present new bundle-type method...
متن کاملA Bundle Method for Solving Convex Non-smooth Minimization Problems
Numerical experiences show that bundle methods are very efficient for solving convex non-smooth optimization problems. In this paper we describe briefly the mathematical background of a bundle method and discuss practical aspects for the numerical implementation. Further, we give a detailed documentation of our implementation and report about numerical tests.
متن کاملInexact Proximal Gradient Methods for Non-convex and Non-smooth Optimization
Non-convex and non-smooth optimization plays an important role in machine learning. Proximal gradient method is one of the most important methods for solving the nonconvex and non-smooth problems, where a proximal operator need to be solved exactly for each step. However, in a lot of problems the proximal operator does not have an analytic solution, or is expensive to obtain an exact solution. ...
متن کامل