- Post Doctoral
MIT Unit Affiliation:
- Data, Systems, and Society
Post Doc Sponsor / Advisor:
Date PhD Completed:
Top 3 Areas of Expertise:
I am a postdoctoral researcher at the Laboratory for Information and Decision Systems of MIT, hosted by Professors Asu Ozdaglar and Pablo Parrilo. Before that I received my PhD from the Courant Institute of New York University, my diploma from Ecole Polytechnique, and my B.Sc. degrees in electrical engineering and mathematics from Bogazici University as a valedictorian.
My interests lie broadly in optimization and computational science driven by applications in large-scale information, decision and infrastructure systems. My work draws and extends ideas and tools from convex optimization, probability and control of systems.
Expected End Date of Post Doctoral Position:
- Incremental and distributed optimization.
- Control and optimization of large-scale dynamical systems and networks.
- Control of dynamical systems with nonconvex/nonsmooth optimization.
This thesis is composed of three independent parts:
Part I concerns spectral and pseudospectral robust stability measures for linear dynamical systems. Popular measures are the H∞ norm, the distance to instability, numerical radius, spectral abscissa and radius, pseudospectral abscissa and radius. Firstly, we develop and analyze the convergence of a new algorithm to approximate the H∞ norm of large sparse systems. Secondly, we tackle the static output feed- back problem, a problem closely related to minimizing the abscissa (largest real part of the roots) over a family of monic polynomials. We show that when there is just one affine constraint on the coefficients of the monic polynomials, this problem is tractable, deriving an explicit formula for the optimizer when it exists and an approximate optimizer otherwise, and giving a method to compute it efficiently. Thirdly, we develop a new Newton-based algorithm for the calculation of the distance to discrete instability and prove that for generic matrices the algorithm is locally quadratically convergent. For the numerical radius, we give a proof of the fact that the Mengi-Overton algorithm is always quadratically convergent. Finally, we give some regularity results on pseudospectra, the pseudospectral abscissa and the pseudospectral radius. These results answer affirmatively a conjecture raised by Lewis & Pang in 2008.
Part II concerns nonsmooth optimization. We study two interesting nonsmooth functions introduced by Nesterov. We characterize Clarke stationary and Mor- dukhovich stationary points of these functions. Nonsmooth optimization algo- rithms have an interesting behavior on the second function, converging very often to a nonminimizing Clarke stationary point that is not Mordukhovich stationary.
Part III concerns the equivalence between one-bit sigma-delta quantization and a recent optimization-based halftoning method. Sigma-delta quantization is a pop- ular method for the analog-to-digital conversion of signals, whereas halftoning is a core process governing most digital printing and many display devices, by which continuous tone images are converted to bi-level images. The halftoning problem was recently formulated as a global optimization problem. We prove that the same objective function is minimized in one-bit sigma-delta quantization.
Top 5 Awards and honors (name of award, date received):
5 Recent Papers:
Please see my research webpage: https://mert.lids.mit.edu/research/