Convergence of a Scholtes-type regularization method for cardinality-constrained optimization problems with an application in sparse robust portfolio optimization

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11230%2F18%3A10375185" target="_blank" >RIV/00216208:11230/18:10375185 - isvavai.cz</a>

Alternative codes found

RIV/67985556:_____/18:00489264 RIV/00216208:11320/18:10375185

Result on the web

<a href="https://doi.org/10.1007/s10589-018-9985-2" target="_blank" >https://doi.org/10.1007/s10589-018-9985-2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10589-018-9985-2" target="_blank" >10.1007/s10589-018-9985-2</a>

Result language

angličtina

Original language name

Convergence of a Scholtes-type regularization method for cardinality-constrained optimization problems with an application in sparse robust portfolio optimization

Original language description

We consider general nonlinear programming problems with cardinality constraints. By relaxing the binary variables which appear in the natural mixed-integer programming formulation, we obtain an almost equivalent nonlinear programming problem, which is thus still difficult to solve. Therefore, we apply a Scholtes-type regularization method to obtain a sequence of easier to solve problems and investigate the convergence of the obtained KKT points. We show that such a sequence converges to an S-stationary point, which corresponds to a local minimizer of the original problem under the assumption of convexity. Additionally, we consider portfolio optimization problems where we minimize a risk measure under a cardinality constraint on the portfolio. Various risk measures are considered, in particular Value-at-Risk and Conditional Value-at-Risk under normal distribution of returns and their robust counterparts under moment conditions. For these investment problems formulated as nonlinear programming problems with cardinality constraints we perform a numerical study on a large number of simulated instances taken from the literature and illuminate the computational performance of the Scholtes-type regularization method in comparison to other considered solution approaches: a mixed-integer solver, a direct continuous reformulation solver and the Kanzow-Schwartz regularization method, which has already been applied to Markowitz portfolio problems.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10102 - Applied mathematics

Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Computational Optimization and Applications

ISSN

0926-6003

e-ISSN

—

Volume of the periodical

70

Issue of the periodical within the volume

2

Country of publishing house

US - UNITED STATES

Number of pages

28

Pages from-to

503-530

UT code for WoS article

000431036800007

EID of the result in the Scopus database

2-s2.0-85042236326