Contributed Session Thu.1.H 2035

Thursday, 10:30 - 12:00 h, Room: H 2035

Cluster 24: Variational analysis [...]

Structure and stability of optimization problems

 

Chair: Jan-J. Ruckmann

 

 

Thursday, 10:30 - 10:55 h, Room: H 2035, Talk 1

Jan-J. Ruckmann
Max-type objective functions: A smoothing procedure and strongly stable stationary points

 

Abstract:
We consider the minimization of a max-type function
over a feasible set M and apply the concept of strongly stable
stationary points to this class of problems. We use a logarithmic
barrier function and construct a family M\gamma of interior point approximations of
M where M\gamma is described by a single smooth inequality
constraint. We show that there is a one-to-one
correspondence between the stationary points (and their corresponding stationary indices) of the original problem and those
with the feasible set M\gamma.

 

 

Thursday, 11:00 - 11:25 h, Room: H 2035, Talk 2

Helmut Gfrerer
Second-order conditions for a class of nonsmooth programs

 

Abstract:
We study infinite dimensional optimization problems with constraints given in form of an inclusion 0 ∈ F(x)-S(x),
where F denotes a smooth mapping and S is a generalized polyhedral multifunction, e.g., the normal cone mapping of a convex polyhedral set. By using advanced techniques of variational analysis we obtain second-order characterizations, both necessary and sufficient, for directional metric subregularity of the constraint mapping. These results can be used to obtain second-order optimality conditions for the optimization problem.

 

 

Thursday, 11:30 - 11:55 h, Room: H 2035, Talk 3

Peter Fusek
On metric regularity of the Kojima function in nonlinear semidefinite programming

 

Abstract:
The one-to-one relation between the points fulfilling the KKT conditions of an optimization problem and the zeros of the corresponding Kojima function is well-known. In the present paper we study the interplay between metric regularity and strong regularity of this a priori nonsmooth function in the context of semidefinite programming.
Having in mind the topological structure of the positive semidefinite cone we identify a class of Lipschitz metrically regular functions which turn out to have coherently oriented B-subdifferentials. This class is broad enough to include the Kojima function corresponding to the nonlinear semidefinite programming problem.

 

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