arXiv subjects

Andrey Tin

Publications and source records attributed to Andrey Tin.

3 recordsLinked to original sources

arXiv2021

Levenberg-Marquardt method and partial exact penalty parameter selection in bilevel optimization

We consider the optimistic bilevel optimization problem, known to have a wide range of applications in engineering, that we transform into a single-level optimization problem by means of the lower-level optimal value function reformulation. Subsequently, based on the partial calmness concept, we build an equation system, which is parameterized by the corresponding partial exact penalization parameter. We then design and analyze a Levenberg-Marquardt method to solve this parametric system of equations. Considering the fact that the selection of the partial exact penalization parameter is a critical issue when numerically solving a bilevel optimization problem, we conduct a careful experimental study to this effect, in the context the Levenberg-Marquardt method, while using the Bilevel Optimization LIBrary (BOLIB) series of test problems.

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arXiv2020

BOLIB: Bilevel Optimization LIBrary of test problems

This chapter presents the Bilevel Optimization LIBrary of the test problems (BOLIB for short), which contains a collection of test problems, with continuous variables, to help support the development of numerical solvers for bilevel optimization. The library contains 173 examples with 138 nonlinear, 24 linear, and 11 simple bilevel optimization problems. This BOLIB collection is probably the largest bilevel optimization library of test problems. Moreover, as the library is computationenabled with the MATLAB m-files of all the examples, it provides a uniform basis for testing and comparing algorithms. The library, together with all the related codes, is freely available at biopt.github.io/bolib.

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arXiv2020

Gauss-Newton-type methods for bilevel optimization

This article studies Gauss-Newton-type methods for over-determined systems to find solutions to bilevel programming problems. To proceed, we use the lower-level value function reformulation of bilevel programs and consider necessary optimality conditions under appropriate assumptions. First under strict complementarity for upper- and lower-level feasibility constraints, we prove the convergence of a Gauss-Newton-type method in computing points satisfying these optimality conditions under additional tractable qualification conditions. Potential approaches to address the shortcomings of the method are then proposed, leading to alternatives such as the pseudo or smoothing Gauss-Newton-type methods for bilevel optimization. Our numerical experiments conducted on 124 examples from the recently released Bilevel Optimization LIBrary (BOLIB) compare the performance of our method under different scenarios and show that it is a tractable approach to solve bilevel optimization problems with continuous variables.

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