S-prosedür ve bazı çeşitleri hakkında

ABSTRACTON THE S-PROCEDURE AND SOME VARIANTSKürşad DerinkuyuusM.S. in Industrial EngineeringSupervisor: Prof. Dr. Mustafa Celebi PınarşJuly, 2004In this thesis, we deal with the S-procedure that corresponds to verifying that theminimum of a quadratic function over constraints consisting of quadratic func-tions is positive. S-procedure is an instrumental tool in control theory and robustoptimization analysis. It is also used in linear matrix inequality (or semi definiteprogramming) reformulations and analysis of quadratic programming. We im-prove an error bound in the Approximate S-Lemma used in establishing levels ofconservatism results for approximate robust counterparts. Moreover we extendthe S-procedure and obtain some general results in this field. Finally, we get abound similar to Nesterov?s bound for trust region subproblem, which consistsin minimizing an indefinite quadratic function subject to a norm-1 constraint byusing the Approximate S-Lemma.Keywords: S-procedure, Approximate S-Lemma, Extended S-procedure, robustoptimization, (conic) quadratic programming.iii