## Invited Session Thu.3.H 1012

#### Thursday, 15:15 - 16:45 h, Room: H 1012

**Cluster 17: Nonsmooth optimization** [...]

### Algorithms for nonsmooth optimization

**Chair: Robert Mifflin**

**Thursday, 15:15 - 15:40 h, Room: H 1012, Talk 1**

**Robert Mifflin**

A first step in designing a VU-algorithm for nonconvex minimization

**Coauthor: Claudia A. Sagastiz'abal**

**Abstract:**

This talk lays the ground work for designing a future VU-type minimization algorithm to run on locally Lipschitz functions for which only one Clarke generalized gradient is known at a point. This entails development of a bundle method V-algorithm that has provable convergence to stationary points for semismooth functions and can make adequate estimates of "V-subspace'' bases in the presence of nonconvexity. Ordinary bundle methods generate consecutive "null steps'' from a "bundle center'' until a "serious step'' point is found, which then becomes the next center. A VU-algorithm is similar except that its serious descent point is "very serious'' which means it defines a good "V-step'' and "U-gradient'' pair for making an additional "U-step'' to the next center. For an objective function of one variable the desired VU- algorithm exists, but it does not extend directly to functions of *n* variables. For convex functions about 20 years worth of proximal point and VU theory had to be developed before a rapidly convergent method for the multivariable case could be defined. For the nonconvex case two ideas from the *n=1* algorithm are adapted to create the desired *n*-variable V-algorithm.

**Thursday, 15:45 - 16:10 h, Room: H 1012, Talk 2**

**Welington Oliveira**

Exploring accuracy and geometry in level bundle methods

**Abstract:**

We consider level bundle methods for minimizing a nonsmooth convex function over a closed convex set. These algorithms only require evaluating the function and a subgradient with a variable accuracy. Besides handling inaccurate oracle information, if the problem is bounded, the methods can take advantage of the feasible set geometry to obtain near-optimal complexity bounds.

**Thursday, 16:15 - 16:40 h, Room: H 1012, Talk 3**

**Adam Ouorou**

Specialized proximal Chebychev center cutting plane algorithm for convex additive functions

**Abstract:**

The author has recently proposed an approach for convex nonsmooth optimization, which regularizes the cutting plane algorithm of Elzinga and Moore. In this talk, this approach is tailored to the case where the objective function is additive. We highlight aspects where this specialization differs from ignoring the structure of the objective function. To assess the approach, we consider some nonlinear multicommodity flows applications in telecommunications, and a comparison with a proximal bundle algorithm.