0489264 20240103215946.820180502235959.9 85042236326 000431036800007 10.1007/s10589-018-9985-2 28 s. P cav_un_epca*02525650926-6003702 (2018)503-530Springer Cardinality constraints Regularization method Scholtes regularization Strong stationarity Sparse portfolio optimization Robust portfolio optimization cav_un_auth*0280972 Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Branda Martin UTIA-B CZ K Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0302028 Bucher M. DE cav_un_auth*0220207 Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Červinka Michal UTIA-B S Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0332700 Schwartz A. DE S http://library.utia.cas.cz/separaty/2018/MTR/branda-0489264.pdf cav_un_auth*0321507 GA15-00735S GA ČR 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. WOS BB 10000 10100 10103 2019 4 4 A hod 4ah 20231122143147.7 RVO:67985556 http://hdl.handle.net/11104/0283708 1 Department of Decision Making Theory UTIA-B 10102 MATHEMATICS, APPLIED S 1 Article Operations Research Management Science|Mathematics Applied MATHEMATICS.APPLIED|OPERATIONSRESEARCH&MANAGEMENTSCIENCE 2.064 0.468 7.4 0.00626 1.078 2485 0.997 1.753 94 Q1 83.341 70.1 Q1 Q2 0.93 Q2 82.48 2018 Soubory v repozitáři: branda-0489264.pdf 85042236326 SCOPUS PUBMED 000431036800007 WOS cav_un_epca*0252565 Computational Optimization and Applications 0926-6003 1573-2894 Roč. 70 č. 2 2018 503 530 Springer