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

Kód výsledku v 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>

Nalezeny alternativní kódy

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

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Computational Optimization and Applications

ISSN

0926-6003

e-ISSN

—

Svazek periodika

70

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

28

Strana od-do

503-530

Kód UT WoS článku

000431036800007

EID výsledku v databázi Scopus

2-s2.0-85042236326