Invited Session Mon.3.H 2035

Monday, 15:15 - 16:45 h, Room: H 2035

Cluster 24: Variational analysis [...]

Lower order exact penalty functions


Chair: Xiaoqi Yang



Monday, 15:15 - 15:40 h, Room: H 2035, Talk 1

Xiaoqi Yang
Optimality conditions via exact penalty functions

Coauthor: Kaiwen Meng


In this presentation, we study KKT optimality conditions for constrained nonlinear programming problems and strong and Mordukhovich stationarities for mathematical programs with complementarity constraints using lp penalty functions with 0 ≤ p ≤ 1. We introduce some optimality indication sets by using contingent derivatives of penalty function terms. Some characterizations of optimality indication sets by virtue of the original problem data are obtained. We show that KKT optimality condition holds at a feasible point if this point is a local minimizer of some lp penalty function with p belonging to the optimality indication set.
Our result on constrained nonlinear programming includes some existing ones in the literature as special cases.



Monday, 15:45 - 16:10 h, Room: H 2035, Talk 2

Boshi Tian
An interior-point l1/2-penalty method for nonlinear programming

Coauthor: Xiaoqi Yang


In this presentation, we solve general nonlinear programming problems by using a quadratic relaxation scheme for their l1/2-lower order penalty problems.
Combining an interior point method, we propose an interior point l1/2-penalty function method, and design some robust algorithms. Using some relaxed constraint qualifications, we obtain first-order optimality conditions of relaxed l1/2-lower order penalty problems. We also carry out numerical experiments for three test problem sets, which contain small scale and medium scale test problems, large scale test problems and optimization problems with different kinds of degenerate constraints, respectively. The comparison of the numerical performance of our method with other existing interior point penalty methods shows that our method in general performs better in terms of CPU time, iteration number, barrier parameter, and penalty parameter.



Monday, 16:15 - 16:40 h, Room: H 2035, Talk 3

Zhangyou Chen
Exact penalty functions for semi-infinite programming

Coauthors: Xiaoqi Yang, Jinchuan Zhou


We study optimality conditions of an inequality constraint semi-infinite optimization problem from the point of view of exact penalty functions. We introduce two types of penalty functions for the semi-infinite optimization problem, l\infty-type and integral-type penalty functions, and investigate their exactness relations as well as their relations with corresponding calmness properties, respectively. We establish first-order optimality conditions for the semi-infinite optimization problem via (esp. lower order) exact penalty functions. Finally, we apply our results to a generalized semi-infinite optimization problem by virtue of a double penalization technique.


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