**Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization**

Humboldt-Universität zu Berlin, WIAS Berlin

#### Dr. P. Dvurechensky

## First-order optimization methods with inexact information about the objective function value and its gradient

**Programm / Abstract:**

In this talk I will discuss first-order methods with inexact oracle for finite-dimensional optimization. Oracle model of optimization methods assumes that, given a point, the oracle returns some information on the objective function at this point. In the case of first-order optimization methods, this information is the function value and its gradient at this point. I will start with convex problems, inexact oracle defined in the work by O. Devolder, F. Glineur, Yu. Nesterov, Math. Prog., 2014, and convergence rates for gradient descent and accelerated gradient descent in this case. I will also describe an extension for non-convex problems. Then I will discuss some ideas on how these methods potentially can be extended and applied for infinite-dimensional problems. If time allows, I will cover other optimization problems and methods, which I work with. Among others, optimal transport problem and an accelerated gradient descent for its solution, randomized optimization methods, such as random coordinate descent and random derivative-free method, variational inequalities, saddle-point problems and first-order methods for their solution.

**Zeit:**

am Mittwoch den 18. April 2018 um 15:00

**Ort:**

Weierstraß-Institut

Mohrenstr. 39

10117 Berlin

Weierstraß-Hörsaal (Raum: 406) 4. Etage

*eingetragen von sek8(sek8@wias-berlin.de, 030 20372595)*

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