Invited Session Mon.2.H 0110

Monday, 13:15 - 14:45 h, Room: H 0110

Cluster 16: Nonlinear programming [...]

Nonlinear optimization II


Chair: Frank E. Curtis and Daniel Robinson



Monday, 13:15 - 13:40 h, Room: H 0110, Talk 1

Daniel Robinson
A primal-dual active-set method for convex QP

Coauthors: Frank Curtis, Zheng Han


We present a rapidly adapting active-set method for solving large-scale strictly convex quadratic optimization problems. In contrast to traditional active-set methods, ours allows for rapid changes in the active set estimate. This leads to rapid identification of the optimal active set, regardless of the initial estimate. Our method is general enough that it can be utilized as a framework for any method for solving convex quadratic optimization problems. Global convergence guarantees are provided for two variants of the framework. Numerical results are also provided, illustrating that our framework is competitive with state-of-the-art solvers on most problems, and is superior on ill-conditioned problems. We attribute these latter benefits to the relationship between the framework and a semi-smooth Newton method.



Monday, 13:45 - 14:10 h, Room: H 0110, Talk 2

Sven Leyffer
Large-scale nonlinear optimization solvers


We describe the development of a suit of tools and solvers for large-scale nonlinearly constrained optimization problems. We emphasize methods that can operate in a matrix-free mode and avoid matrix factorizations. Our framework implements a range fo two-phase active-set methods, that are required, for example, for fast resolves in mixed-integer solvers. In the first phase, we estimate the active set, and in the second phase we perform a Newton step on the active constraints. We show that our framework can be designed in a matrix-free mode, and analyze its convergence properties. We show that allowing a small number of active-set changes in the Newton step improves convergence.



Monday, 14:15 - 14:40 h, Room: H 0110, Talk 3

Elizabeth Wong
Regularized quadratic programming methods for large-scale SQP

Coauthors: Philip E. Gill, Daniel P. Robinson


We present a regularized method for large-scale quadratic programming (QP). The method requires the solution of a sequence of bound-constrained subproblems defined in terms of both the primal and dual variables. The subproblems may be solved using a conventional active-set method, which would involve the solution of a regularized KKT system at each step, or a method based on gradient projection. In the convex case, the solution of the bound-constrained subproblem is also a solution of the QP subproblem for a stabilized sequential quadratic programming (SQP) method. Numerical results are presented.


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