Invited Session Mon.3.H 2051

Monday, 15:15 - 16:45 h, Room: H 2051

Cluster 24: Variational analysis [...]

Some applications of variational analysis


Chair: Nguyen Dong Yen



Monday, 15:15 - 15:40 h, Room: H 2051, Talk 1

Mau Nam Nguyen
Variational analysis of minimal time functions with unbounded dynamics and generalized smallest enclosing circle problems


The smallest enclosing circle problem introduced in the 19th century by J. J. Sylvester asks for the circle of smallest radius enclosing a given set of finite points in the plane. In this talk we will present new results on variational analysis of of minimal time functions generated by unbounded constant dynamics and discuss their applications to generalized versions of of the smallest enclosing circle problem. This approach continues our effort in applying variational analysis to the well-established field of facility location.



Monday, 15:45 - 16:10 h, Room: H 2051, Talk 2

Andrew Craig Eberhard
Approaches to optimality conditions using nonsmooth and variational methods

Coauthors: Boris Mordukhovich, Charles Pearce, Robert Wenczel


In this talk we survey a number of approaches to the development of optimality conditions that delay the introduction of regularity conditions. In doing so they generalize the standard Lagrangian optimality conditions and second order sufficiency conditions in various ways. The infimal regularization and a mixture of subhessian and coderivative like techniques are used in combination with variational methods.



Monday, 16:15 - 16:40 h, Room: H 2051, Talk 3

Gue Myung Lee
On constraint qualifications for mathematical programs with equilibrium constraints

Coauthor: Chieu Nguyen Huy


Mathematical program with equilibrium constraints (shortly, MPEC) has been the subject of intensive research during the last decades. We introduce a relaxed version of a constraint qualification for the MPEC formulated as optimization problems with complementarity constraints. We present that the relaxed version is an MPEC-constraint qualification for M-stationarity. Using the limiting second-order subdifferential for C1,1 functions, we show that the relaxed version is strong enough to ensure the validity of a local MPEC-error bound under a certain additional assumption.


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