Combining approximation and exact penalty in hierarchical programming

被引：3

作者：

Bigi, Giancarlo ^{[1
]}

Lampariello, Lorenzo ^{[2
]}

Sagratella, Simone ^{[3
]}

机构：

[1] Univ Pisa, Dept Comp Sci, Pisa, Italy

[2] Roma Tre Univ, Dept Business Studies, Rome, Italy

[3] Sapienza Univ Rome, Dept Comp Control & Management Engn Antonio Ruber, Rome, Italy

来源：

OPTIMIZATION | 2022年 / 71卷 / 08期

关键词：

Hierarchical programming; optimization problems with variational inequality constraints; approximation approaches; penalty techniques; DISTRIBUTED METHODS; BILEVEL PROGRAMS; ALGORITHMS; PARALLEL;

D O I：

10.1080/02331934.2021.1939336

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We address the minimization of an objective function over the solution set of a (non-parametric) lower-level variational inequality. This problem is a special instance of semi-infinite programs and encompasses, as particular cases, simple (smooth) bilevel and equilibrium selection problems. We resort to a suitable approximated version of the hierarchical problem. We show that this, on the one hand, does not perturb the original (exact) program 'too much', on the other hand, allows one to rely on some suitable exact penalty approaches whose convergence properties are established.

引用

页码：2403 / 2419

页数：17

共 47 条

[1] Sufficient conditions to compute any solution of a quasivariational inequality via a variational inequality [J].