Invited Session Wed.1.H 2051

Wednesday, 10:30 - 12:00 h, Room: H 2051

Cluster 24: Variational analysis [...]

Quadratic and polynomial optimization


Chair: Guoyin Li



Wednesday, 10:30 - 10:55 h, Room: H 2051, Talk 1

Gwi Soo Kim
On ε-saddle point theorems for robust convex optimization problems

Coauthor: Gue Myung Lee


In this talk, we consider ε-approximate solutions for a convex optimization problem in the face of data uncertainty, which is called a robust convex optimization problem. Using robust optimization approach(worst-case approach), we define ε-saddle points for ε-approximate solutions of the robust convex optimization problem. We prove a sequential ε-saddle point theorem for an ε-approximate solution of a robust convex optimization problem which holds without any constraint qualification, and then we give an ε-saddle point theorem for an ε-approximate solution which holds under a weaken constraint qualification.



Wednesday, 11:30 - 11:55 h, Room: H 2051, Talk 3

Guoyin Li
Error bound for classes of polynomial systems and its applications: A variational analysis approach

Coauthor: Boris Mordukhovich


Error bound is an important tool which provides an effective estimation of the distance from an arbitrary point to a set in terms of a computable "residual function''. The study of error bound plays an important role in the convergence analysis of optimization algorithms and accurate identification of active constraints. In this talk, we are interested in error bound for classes of polynomial systems. Using variational analysis technique, we first show that global Lipschitz type error bound holds for a convex polynomial under Slater condition. When Slater condition is not satisfied, we establish a global Hölderian type error bound with an explicit estimate of the Hölderian exponent extending the known results for convex quadratic functions. Next, we extend these results to some classes of nonconvex system including piecewise convex polynomials and composite polynomial systems. Finally, as an application, we apply the error bound results to provide a quantitative convergence analysis of the classical proximal point method.


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