On Criticality of Lagrange Multipliers for Optimization Problems

Thời gian: 14:30 đến 16:00 ngày 21/10/2021, 14:30 đến 16:00 ngày 28/10/2021,

Địa điểm: C101, VIASM

Báo cáo viên: TS Nguyễn Thị Vân Hằng - Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ VN

Tóm tắt:

In these talks, we first recall the notion of critical and noncritical multiplier introduced by Izmailov for NLPs, its characterizations and application to study of numerical methods for this class of optimization problems. We then introduce and study the notion extended for the class of composite optimization problems by making use of generalized second-order derivatives such as second epi-derivative and subgradient graphical derivative. Finally, we discuss some open questions on studying convergence of augmented Lagrangian methods and stabilized sequential quadratic programming method for composite optimization problems under the noncriticality assumption instead of the classical second-order sufficient optimality condition (SOSC).

Selected references:
[Izmailov and Solodov, 2012] Stabilized SQP: revisited.
[Izmailov et al., 2015] Local convergence of the method of multipliers for variational and optimization problems under the noncriticality assumption.
[Sarabi, 2021] Primal superlinear convergence of SQP methods in piecewise linear-quadratic composite optimization.