 CARMA RHD MEETING
 Speaker: Arnab Sur, Industrial Engineering and Operations Research (IEOR), Indian Institute of Technology Bombay
 Title: Mstationarity Concept for a Class of Stochastic MPCC Problems
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 12:00 pm, Thu, 19^{th} Jun 2014
 Abstract:
In this talk we are going to discuss the importance of Mstationary conditions for a special class of onestage stochastic mathematical programming problem with complementarity constraints (SMPCC, for short). Mstationarity concept is well known for deterministic MPCC problems. Now using the results of deterministic MPCC problems we can easily derive the Mstationarity for SMPCC problems under some well known constraint qualifications. It is well observed that under MPCClinear independence constraint qualification we obtain strong stationarity conditions at a local minimum, which is a stronger notion than Mstationarity. Same result cab be derived for SMPCC problems under SMPCCLICQ. Then the question that will arise is: What is the importance to study Mstationarity under the assumption of SMPCCLICQ. To answer this question we have to discuss sample average approximation (SAA) method, which is a common technique to solve stochastic optimization problems. Here one has to discretize the underlying probability space and then using the strong Law of Large Numbers one has to approximate the expectation functionals. Now the main result of this discussion as follows: If we consider a sequence of Mtype Fritz John points of the SAA problems then any accumulation point of this sequence will be an Mstationarity point under SMPCCLICQ. But this kind of result, in general, does not hold for strong stationarity conditions.
 [Permanent link]
