טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentBoni Odellia
SubjectRobust Solutions of Conic Quadratic Problems
DepartmentDepartment of Industrial Engineering and Management
Supervisor Professor Emeritus Aharon Ben-Tal
Full Thesis textFull thesis text - English Version


Abstract

Robust optimization aims to find solutions which are feasible for every realization of the uncertain data affecting the optimization problem.


This work extends the methodology of Robust Optimization in three important directions.


The first is finding robust solutions to conic quadratic problems. The results known so far assumed independency of the uncertainties affecting both sides of the conic quadratic constraint. We present applications for which this assumption is inherently false and develop a semidefinite approximation to the robust counterpart relieving the independency assumption. Applying this approximation to problems in finance and robotics shows that the level of the approximation is good and performs better than other recently introduced approximations.


The second direction deals with multi-stage conic quadratic and semidefinite problems, where one can take advantage of the fact that part of the decision variables may not have to be determined beforehand (“adjustable variables”). Up till now, this approach was incorporated only into uncertain linear problems. We incorporate it into robust conic quadratic and semidefinite optimization. The new methodology is applied to a problem of subway route design and a problem in supply chain management. The results are compared to the nominal and non-adjustable robust solutions. They demonstrate that the adjustable robust solution maintains feasibility for all realizations, and obtains better objective function values.


Finally, we present a model of “mixed uncertainty” where the optimization problem is affected by bounded perturbations as well as random ones. In these cases the aim is to ensure feasibility of the solution for all bounded perturbations and for most probable random perturbations. We develop approximated robust counterparts for linear, conic quadratic and semidefinite constraints affected by mixed uncertainty.