Optimization Theory

Optimization Theory

Tonguç Ünlüyurt
Applied Combinatorial Optimization

Combinatorial optimization involves optimization over discrete sets where a feasible solution is a combinatorial object such as a graph, permutation, set etc. Such problems are motivated by a diverse range of applications including logistics, manufacturing and telecommunications systems.

We consider various “optimal search” problems where the goal is to detect a hidden object by utilizing costly tests. The goal could be minimizing the expected cost or optimizing another performance metric regarding the accuracy of the conclusion. One can also consider other variations where the goal is classify an unknown Boolean vector correctly with the minimum cost.

We also study frequency assignment and routing problems in wireless telecommunication networks.

Ezgi Karabulut Türkseven
Distributed Optimization

Distributed optimization is an area that studies decentralized solution methods for optimization problems, whose data, for reasons such as data privacy or processor capacity limitations, is not centralized.

Our research is on obtaining the existing performance guarantees with limited data sharing. In this framework, we work on problems such as discrete resource allocation, or focus on learning from the limited information shared among agents.

Burak Kocuk
Global Optimization in Engineering Applications

Engineering systems are ubiquitous, and they are evolving into more and more complicated structures. Engineering optimization is concerned with designing and operating such systems in the best possible way.

Engineering optimization problems typically belong to an optimization problem class called mixed-integer nonlinear programming. The solution of this challenging class of problems requires specialized global optimization techniques, which need to combine both theoretical and algorithmic aspects. Our research involves developing such solution methods for applications arising in the following areas: electrical engineering, chemical engineering, financial engineering, material science and biology.

Esra Koca
Optimization under Uncertainty

Most of the real world problems include uncertainties forcing the decision makers to act before observing uncertain events. Stochastic programming considers these uncertainties in the modeling stage and helps the decision makers to react after the uncertain events are observed. We work on two stage and multi-stage stochastic optimization problems emerging in production and distribution systems, and develop efficient solution methods to solve these large scale optimization problems.