Invited Session Wed.1.H 0110

Wednesday, 10:30 - 12:00 h, Room: H 0110

Cluster 16: Nonlinear programming [...]

Trust-region methods and nonlinear programming


Chair: Henry Wolkowicz and Ting Kei Pong



Wednesday, 10:30 - 10:55 h, Room: H 0110, Talk 1

Ya-xiang Yuan
Optimality conditions and smoothing trust region newton method for non-lipschitz optimization

Coauthors: Xiaojun Chen, Lingfeng Niu



Regularized minimization problems with nonconvex, nonsmooth, perhaps non-Lipschitz penalty functions have
attracted considerable attention in recent years, owing to their wide
applications in image restoration, signal reconstruction and
variable selection. In this paper, we derive affine-scaled second order necessary
and sufficient conditions for local minimizers of such
minimization problems. Moreover, we propose a global convergent
smoothing trust region Newton method which can find
a point satisfying the affine-scaled second order necessary
optimality condition from any starting point.
Numerical examples are given to illustrate the efficiency of the optimality conditions and the smoothing
trust region Newton method.



Wednesday, 11:00 - 11:25 h, Room: H 0110, Talk 2

Ting Kei Pong
Generalized trust region subproblem: Analysis and algorithm

Coauthor: Henry Wolkowicz


The trust region subproblem (TRS) is the minimization of a (possibly nonconvex) quadratic function over a ball. It is the main step of the trust region method for unconstrained optimization, and is a basic tool for regularization. In this talk, we consider a generalization of the TRS, where the ball constraint is replaced by a general quadratic constraint with both upper and lower bounds. We characterize optimality under a mild constraint qualification and extend an efficient algorithm for TRS proposed by Rendl and Wolkowicz to this setting.
% This is an ongoing work with Henry Wolkowicz.



Wednesday, 11:30 - 11:55 h, Room: H 0110, Talk 3

Yuen-Lam Vris Cheung
Solving a class of quadratically constrained semidefinite prgramming problems with application to structure based drug design problem

Coauthors: Forbes Burkowski, Henry Wolkowicz


We consider a class of quadratically constrained semidefinite programming (SDP) problems arising from a structure based drug design problem.
In graph theoretical terms, we aim at finding a realization of a graph with fixed-length edges, such that the sum of the distances between some of the non-adjacent vertices is minimized and the graph is realized in a Euclidean space of prescribed dimension. This problem can be seen as a Euclidean distance matrix completion problem and can be phrased as a semidefinite programming problem (SDP) with quadratic constraints. In order to provide approximate solutions to the special class of quadratically constrained SDP problems, we extend the techniques for solving two trust region problems (TTRS) and indefinite trust region problems to the SDP. We also present some preliminary numerical results on the structure based drug design problem.


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