**Angelia Nedich**

**Industrial and Enterprise Systems Engineering **

**University of Illinois at Urbana-Champaign**

**Distributed Optimization in Directed Graphs: Push-Sum Based Algorithms**

We consider distributed optimization by a collection of nodes, each having access to its own convex function, whose collective goal is to minimize the sum of the functions. The communications between nodes are described by a time-varying sequence of directed graphs, which is uniformly strongly connected. For such communications, assuming that every node knows its out-degree, we develop a broadcast-based algorithm, termed the subgradient-push, which steers every node to an optimal value under a standard assumption of subgradient boundedness. The subgradient-push requires no knowledge of either the number of agents or the graph sequence to implement. Our analysis shows that the subgradient-push algorithm converges at a rate of O(ln t/t). The proportionality constant in the convergence rate depends on the initial values at the nodes, the subgradient norms and, more interestingly, on both the speed of the network information diffusion and the imbalances of influence among the nodes. This is joint work with Prof. A. Olshevsky.

Angelia Nedich received her B.S. degree from the University of Montenegro (1987) and M.S. degree from the University of Belgrade (1990), both in Mathematics. She received her Ph.D. degrees from Moscow State University (1994) in Mathematics and Mathematical Physics, and from Massachusetts Institute of Technology in Electrical Engineering and Computer Science (2002). She has been at the BAE Systems Advanced Information Technology from 2002-2006. In Fall 2006, she has joined the Department of Industrial and Enterprise Systems Engineering at the University of Illinois at Urbana-Champaign, USA. She is a recipient of the NSF CAREER Award 2007 in Operations Research for her work in distributed multi-agent optimization.

Prior to the colloquium, coffee will be served in FO 2.404

Sponsored by the Department of Mathematical Sciences

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