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Journal articles on the topic 'Cardinality constrained optimization'

Author: Grafiati

Published: 10 March 2023

Last updated: 31 July 2025

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1

Kanzow, Christian, Andreas B. Raharja, and Alexandra Schwartz. "An Augmented Lagrangian Method for Cardinality-Constrained Optimization Problems." Journal of Optimization Theory and Applications 189, no. 3 (2021): 793–813. http://dx.doi.org/10.1007/s10957-021-01854-7.

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AbstractA reformulation of cardinality-constrained optimization problems into continuous nonlinear optimization problems with an orthogonality-type constraint has gained some popularity during the last few years. Due to the special structure of the constraints, the reformulation violates many standard assumptions and therefore is often solved using specialized algorithms. In contrast to this, we investigate the viability of using a standard safeguarded multiplier penalty method without any problem-tailored modifications to solve the reformulated problem. We prove global convergence towards an

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2

Bertsimas, Dimitris, and Romy Shioda. "Algorithm for cardinality-constrained quadratic optimization." Computational Optimization and Applications 43, no. 1 (2007): 1–22. http://dx.doi.org/10.1007/s10589-007-9126-9.

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3

Kanzow, Christian, Andreas B. Raharja, and Alexandra Schwartz. "Sequential optimality conditions for cardinality-constrained optimization problems with applications." Computational Optimization and Applications 80, no. 1 (2021): 185–211. http://dx.doi.org/10.1007/s10589-021-00298-z.

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AbstractRecently, a new approach to tackle cardinality-constrained optimization problems based on a continuous reformulation of the problem was proposed. Following this approach, we derive a problem-tailored sequential optimality condition, which is satisfied at every local minimizer without requiring any constraint qualification. We relate this condition to an existing M-type stationary concept by introducing a weak sequential constraint qualification based on a cone-continuity property. Finally, we present two algorithmic applications: We improve existing results for a known regularization m

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4

Stephan, Rüdiger. "Cardinality constrained combinatorial optimization: Complexity and polyhedra." Discrete Optimization 7, no. 3 (2010): 99–113. http://dx.doi.org/10.1016/j.disopt.2010.03.002.

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5

Cai, L. "Parameterized Complexity of Cardinality Constrained Optimization Problems." Computer Journal 51, no. 1 (2007): 102–21. http://dx.doi.org/10.1093/comjnl/bxm086.

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6

Bacanin, Nebojsa, and Milan Tuba. "Firefly Algorithm for Cardinality Constrained Mean-Variance Portfolio Optimization Problem with Entropy Diversity Constraint." Scientific World Journal 2014 (2014): 1–16. http://dx.doi.org/10.1155/2014/721521.

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Portfolio optimization (selection) problem is an important and hard optimization problem that, with the addition of necessary realistic constraints, becomes computationally intractable. Nature-inspired metaheuristics are appropriate for solving such problems; however, literature review shows that there are very few applications of nature-inspired metaheuristics to portfolio optimization problem. This is especially true for swarm intelligence algorithms which represent the newer branch of nature-inspired algorithms. No application of any swarm intelligence metaheuristics to cardinality constrai

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7

Xu, Fengmin, Yuhong Dai, Zhihu Zhao, and Zongben Xu. "Efficient projected gradient methods for cardinality constrained optimization." Science China Mathematics 62, no. 2 (2018): 245–68. http://dx.doi.org/10.1007/s11425-016-9124-0.

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8

Sadjadi, Seyed Jafar, Mohsen Gharakhani, and Ehram Safari. "Robust optimization framework for cardinality constrained portfolio problem." Applied Soft Computing 12, no. 1 (2012): 91–99. http://dx.doi.org/10.1016/j.asoc.2011.09.006.

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9

Shaw, Dong X., Shucheng Liu, and Leonid Kopman. "Lagrangian relaxation procedure for cardinality-constrained portfolio optimization." Optimization Methods and Software 23, no. 3 (2008): 411–20. http://dx.doi.org/10.1080/10556780701722542.

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10

Febrianti, Werry, Kuntjoro Adji Sidarto, and Novriana Sumarti. "Solving Constrained Mean-Variance Portfolio Optimization Problems Using Spiral Optimization Algorithm." International Journal of Financial Studies 11, no. 1 (2022): 1. http://dx.doi.org/10.3390/ijfs11010001.

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Portfolio optimization is an activity for balancing return and risk. In this paper, we used mean-variance (M-V) portfolio models with buy-in threshold and cardinality constraints. This model can be formulated as a mixed integer nonlinear programming (MINLP) problem. To solve this constrained mean-variance portfolio optimization problem, we propose the use of a modified spiral optimization algorithm (SOA). Then, we use Bartholomew-Biggs and Kane’s data to validate our proposed algorithm. The results show that our proposed algorithm can be an efficient tool for solving this portfolio optimizatio

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11

Leung, Man-Fai, and Jun Wang. "Cardinality-constrained portfolio selection based on collaborative neurodynamic optimization." Neural Networks 145 (January 2022): 68–79. http://dx.doi.org/10.1016/j.neunet.2021.10.007.

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12

Homchenko, A. A., C. Lucas, S. V. Mironov, and S. P. Sidorov. "Heuristic Algorithm for the Cardinality Constrained Portfolio Optimization Problem." Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics 13, no. 2(2) (2013): 92–95. http://dx.doi.org/10.18500/1816-9791-2013-13-2-2-92-95.

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13

吴, 霜. "An Interior Penalty Algorithm for Cardinality-Constrained Optimization Problems." Advances in Applied Mathematics 13, no. 01 (2024): 21–28. http://dx.doi.org/10.12677/aam.2024.131003.

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14

AlMaadeed, Temadher, Tahereh Khodamoradi, Maziar Salahi, and Abdelouahed Hamdi. "Penalty ADM Algorithm for Cardinality Constrained Mean-Absolute Deviation Portfolio Optimization." Statistics, Optimization & Information Computing 10, no. 3 (2022): 775–88. http://dx.doi.org/10.19139/soic-2310-5070-1312.

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In this paper, we study the cardinality constrained mean-absolute deviation portfolio optimization problem with risk-neutral interest rate and short-selling. We enhance the model by adding extra constraints to avoid investing in those stocks without short-selling positions. Also, we further enhance the model by determining the short rebate based on the return. The penalty alternating direction method is used to solve the mixed integer linear model. Finally, numerical experiments are provided to compare all models in terms of Sharpe ratios and CPU times using the data set of the NASDAQ and S&am

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15

Monge, Juan F. "Equally weighted cardinality constrained portfolio selection via factor models." Optimization Letters 14, no. 8 (2020): 2515–38. http://dx.doi.org/10.1007/s11590-020-01571-6.

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16

Kresta, Aleš. "SOLVING CARDINALITY CONSTRAINED PORTFOLIO OPTIMIZATION PROBLEM BY BINARY PARTICLE SWARM OPTIMIZATION ALGORITHM." Acta academica karviniensia 11, no. 3 (2011): 24–33. http://dx.doi.org/10.25142/aak.2011.043.

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17

王, 雪纯. "A Relaxed Constant Positive Linear Dependence Constraint Qualification for Cardinality-Constrained Optimization Problems." Advances in Applied Mathematics 12, no. 12 (2023): 5018–26. http://dx.doi.org/10.12677/aam.2023.1212493.

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18

Ahmadi, Ardeshir, and Hamed Davari-Ardakani. "A multistage stochastic programming framework for cardinality constrained portfolio optimization." Numerical Algebra, Control & Optimization 7, no. 3 (2017): 359–77. http://dx.doi.org/10.3934/naco.2017023.

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19

Mozafari, Marzieh. "A new IPSO-SA approach for cardinality constrained portfolio optimization." International Journal of Industrial Engineering Computations 2, no. 2 (2011): 249–62. http://dx.doi.org/10.5267/j.ijiec.2011.01.004.

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20

Kalayci, Can B., Olcay Polat, and Mehmet A. Akbay. "An efficient hybrid metaheuristic algorithm for cardinality constrained portfolio optimization." Swarm and Evolutionary Computation 54 (May 2020): 100662. http://dx.doi.org/10.1016/j.swevo.2020.100662.

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21

Raith, Andrea, Marie Schmidt, Anita Schöbel, and Lisa Thom. "Multi-objective minmax robust combinatorial optimization with cardinality-constrained uncertainty." European Journal of Operational Research 267, no. 2 (2018): 628–42. http://dx.doi.org/10.1016/j.ejor.2017.12.018.

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22

Gao, Jianjun, and Duan Li. "A polynomial case of the cardinality-constrained quadratic optimization problem." Journal of Global Optimization 56, no. 4 (2012): 1441–55. http://dx.doi.org/10.1007/s10898-012-9853-z.

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23

Kobayashi, Ken, Yuichi Takano, and Kazuhide Nakata. "Bilevel cutting-plane algorithm for cardinality-constrained mean-CVaR portfolio optimization." Journal of Global Optimization 81, no. 2 (2021): 493–528. http://dx.doi.org/10.1007/s10898-021-01048-5.

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24

Maringer, Dietmar, and Hans Kellerer. "Optimization of cardinality constrained portfolios with a hybrid local search algorithm." OR Spectrum 25, no. 4 (2003): 481–95. http://dx.doi.org/10.1007/s00291-003-0139-1.

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25

Ruiz-Torrubiano, Rubén, and Alberto Suárez. "A memetic algorithm for cardinality-constrained portfolio optimization with transaction costs." Applied Soft Computing 36 (November 2015): 125–42. http://dx.doi.org/10.1016/j.asoc.2015.06.053.

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26

Xu, Fengmin, Zhaosong Lu, and Zongben Xu. "An efficient optimization approach for a cardinality-constrained index tracking problem." Optimization Methods and Software 31, no. 2 (2015): 258–71. http://dx.doi.org/10.1080/10556788.2015.1062891.

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27

Rujeerapaiboon, Napat, Kilian Schindler, Daniel Kuhn, and Wolfram Wiesemann. "Size Matters: Cardinality-Constrained Clustering and Outlier Detection via Conic Optimization." SIAM Journal on Optimization 29, no. 2 (2019): 1211–39. http://dx.doi.org/10.1137/17m1150670.

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28

Jiang, Tao, Shuo Wang, Ruochen Zhang, et al. "An inexact l2-norm penalty method for cardinality constrained portfolio optimization." Engineering Economist 64, no. 3 (2019): 289–97. http://dx.doi.org/10.1080/0013791x.2019.1636169.

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29

Murray, Walter, and Howard Shek. "A local relaxation method for the cardinality constrained portfolio optimization problem." Computational Optimization and Applications 53, no. 3 (2012): 681–709. http://dx.doi.org/10.1007/s10589-012-9471-1.

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30

Chen, Zhiping, Xinkai Zhuang, and Jia Liu. "A Sustainability-Oriented Enhanced Indexation Model with Regime Switching and Cardinality Constraint." Sustainability 11, no. 15 (2019): 4055. http://dx.doi.org/10.3390/su11154055.

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Enhanced indexation is an active portfolio management strategy aimed to find a portfolio outperforming a market index. To ensure stable returns and to avoid extreme losses, a sensible enhanced indexation model should be sustainable, where the parameters of the model should be adjusted adaptively according to the market environment. Hence, in this paper, we propose a novel sustainable regime-based cardinality constrained enhanced indexation (RCEI) model, where different benchmarks and cardinalities can be imposed under different market regimes. By using historical observations, the RCEI model i

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31

Baykasoğlu, Adil, Mualla Gonca Yunusoglu, and F. Burcin Özsoydan. "A GRASP based solution approach to solve cardinality constrained portfolio optimization problems." Computers & Industrial Engineering 90 (December 2015): 339–51. http://dx.doi.org/10.1016/j.cie.2015.10.009.

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32

Zhao, Hong, Zong-Gan Chen, Zhi-Hui Zhan, Sam Kwong, and Jun Zhang. "Multiple populations co-evolutionary particle swarm optimization for multi-objective cardinality constrained portfolio optimization problem." Neurocomputing 430 (March 2021): 58–70. http://dx.doi.org/10.1016/j.neucom.2020.12.022.

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33

Zhao, Hong, Zong-Gan Chen, Zhi-Hui Zhan, Sam Kwong, and Jun Zhang. "Multiple populations co-evolutionary particle swarm optimization for multi-objective cardinality constrained portfolio optimization problem." Neurocomputing 430 (March 2021): 58–70. http://dx.doi.org/10.1016/j.neucom.2020.12.022.

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34

Avci, Mualla Gonca, and Mustafa Avci. "An empirical analysis of the cardinality constrained expectile-based VaR portfolio optimization problem." Expert Systems with Applications 186 (December 2021): 115724. http://dx.doi.org/10.1016/j.eswa.2021.115724.

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35

Lee, Taehan, and Changhyun Kwon. "A short note on the robust combinatorial optimization problems with cardinality constrained uncertainty." 4OR 12, no. 4 (2014): 373–78. http://dx.doi.org/10.1007/s10288-014-0270-7.

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36

Boudt, Kris, and Chunlin Wan. "The effect of velocity sparsity on the performance of cardinality constrained particle swarm optimization." Optimization Letters 14, no. 3 (2019): 747–58. http://dx.doi.org/10.1007/s11590-019-01398-w.

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37

Shiratori, Tomokaze, and Yuichi Takano. "DC algorithm for estimation of sparse Gaussian graphical models." PLOS ONE 19, no. 12 (2024): e0315740. https://doi.org/10.1371/journal.pone.0315740.

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Sparse estimation of a Gaussian graphical model (GGM) is an important technique for making relationships between observed variables more interpretable. Various methods have been proposed for sparse GGM estimation, including the graphical lasso that uses the ℓ1 norm regularization term, and other methods that use nonconvex regularization terms. Most of these methods approximate the ℓ0 (pseudo) norm by more tractable functions; however, to estimate more accurate solutions, it is preferable to directly use the ℓ0 norm for counting the number of nonzero elements. To this end, we focus on sparse es

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38

Kaucic, Massimiliano, Renato Pelessoni, and Filippo Piccotto. "An Automated Decision Support System for Portfolio Allocation Based on Mutual Information and Financial Criteria." Entropy 27, no. 5 (2025): 480. https://doi.org/10.3390/e27050480.

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This paper introduces a two-phase decision support system based on information theory and financial practices to assist investors in solving cardinality-constrained portfolio optimization problems. Firstly, the approach employs a stock-picking procedure based on an interactive multi-criteria decision-making method (the so-called TODIM method). More precisely, the best-performing assets from the investable universe are identified using three financial criteria. The first criterion is based on mutual information, and it is employed to capture the microstructure of the stock market. The second on

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39

Sadigh, Ali Naimi, Hadi Mokhtari, Mehdi Iranpoor, and S. M. T. Fatemi Ghomi. "Cardinality Constrained Portfolio Optimization Using a Hybrid Approach Based on Particle Swarm Optimization and Hopfield Neural Network." Advanced Science Letters 17, no. 1 (2012): 11–20. http://dx.doi.org/10.1166/asl.2012.3666.

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40

Wang, Hao, Michael Emmerich, André Deutz, Víctor Adrián Sosa Hernández, and Oliver Schütze. "The Hypervolume Newton Method for Constrained Multi-Objective Optimization Problems." Mathematical and Computational Applications 28, no. 1 (2023): 10. http://dx.doi.org/10.3390/mca28010010.

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Recently, the Hypervolume Newton Method (HVN) has been proposed as a fast and precise indicator-based method for solving unconstrained bi-objective optimization problems with objective functions. The HVN is defined on the space of (vectorized) fixed cardinality sets of decision space vectors for a given multi-objective optimization problem (MOP) and seeks to maximize the hypervolume indicator adopting the Newton–Raphson method for deterministic numerical optimization. To extend its scope to non-convex optimization problems, the HVN method was hybridized with a multi-objective evolutionary algo

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41

Akbay, Mehmet Anil, Can B. Kalayci, and Olcay Polat. "A parallel variable neighborhood search algorithm with quadratic programming for cardinality constrained portfolio optimization." Knowledge-Based Systems 198 (June 2020): 105944. http://dx.doi.org/10.1016/j.knosys.2020.105944.

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42

Guijarro, Francisco. "A similarity measure for the cardinality constrained frontier in the mean–variance optimization model." Journal of the Operational Research Society 69, no. 6 (2018): 928–45. http://dx.doi.org/10.1057/s41274-017-0276-6.

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43

Monaco, Maria Flavia, Marcello Sammarra, and Luigi Moccia. "Some observations about the extreme points of the Generalized Cardinality-Constrained Shortest Path Problem polytope." Optimization Letters 2, no. 4 (2008): 577–85. http://dx.doi.org/10.1007/s11590-008-0084-7.

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44

Spaeh, Fabian Christian, Alina Ene, and Huy Nguyen. "Online and Streaming Algorithms for Constrained k-Submodular Maximization." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 19 (2025): 20567–74. https://doi.org/10.1609/aaai.v39i19.34266.

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Constrained k-submodular maximization is a general framework that captures many discrete optimization problems such as ad allocation, influence maximization, personalized recommendation, and many others. In many of these applications, datasets are large or decisions need to be made in an online manner, which motivates the development of efficient streaming and online algorithms. In this work, we develop single-pass streaming and online algorithms for constrained k-submodular maximization with both monotone and general (possibly non-monotone) objectives subject to cardinality and knapsack const

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45

Zheng, Xiaojin, Xiaoling Sun, Duan Li, and Jie Sun. "Successive convex approximations to cardinality-constrained convex programs: a piecewise-linear DC approach." Computational Optimization and Applications 59, no. 1-2 (2013): 379–97. http://dx.doi.org/10.1007/s10589-013-9582-3.

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46

Gong, Wei, Shuhan Lou, Liyuan Deng, Peng Yi, and Yiguang Hong. "Efficient Multi-Target Localization Using Dynamic UAV Clusters." Sensors 25, no. 9 (2025): 2857. https://doi.org/10.3390/s25092857.

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This paper proposes a dynamic unmanned aerial vehicle (UAV) clustering model for multi-target localization in complex 3D environments, where mobility-aware cluster formation is integrated to enhance collaborative localization accuracy. We derive the Cramér–Rao lower bound (CRLB) for localization performance analysis under measurement and motion-induced uncertainties. To solve the NP-hard clustering problem, we develop the MDQPSO-ASA algorithm, which combines multi-swarm discrete quantum-inspired particle swarm optimization with adaptive simulated annealing, incorporating a repair mechanism to

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47

SHOUHENG, TUO, and HE HONG. "Solving Complex Cardinality Constrained Mean-Variance Portfolio Optimization Problems Using Hybrid HS and TLBO Algorithm." ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH 52, no. 3/2018 (2018): 231–48. http://dx.doi.org/10.24818/18423264/52.3.18.16.

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48

Dell'Amico, Mauro, Manuel Iori, and Silvano Martello. "Heuristic Algorithms and Scatter Search for the Cardinality Constrained P│CmaxProblem." Journal of Heuristics 10, no. 2 (2004): 169–204. http://dx.doi.org/10.1023/b:heur.0000026266.07036.da.

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49

Djelassi, Hatim, and Alexander Mitsos. "Global Solution of Semi-infinite Programs with Existence Constraints." Journal of Optimization Theory and Applications 188, no. 3 (2021): 863–81. http://dx.doi.org/10.1007/s10957-021-01813-2.

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AbstractWe consider what we term existence-constrained semi-infinite programs. They contain a finite number of (upper-level) variables, a regular objective, and semi-infinite existence constraints. These constraints assert that for all (medial-level) variable values from a set of infinite cardinality, there must exist (lower-level) variable values from a second set that satisfy an inequality. Existence-constrained semi-infinite programs are a generalization of regular semi-infinite programs, possess three rather than two levels, and are found in a number of applications. Building on our previo

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50

Du, Bo, and Hong Zhou. "A Robust Optimization Approach to the Multiple Allocation p-Center Facility Location Problem." Symmetry 10, no. 11 (2018): 588. http://dx.doi.org/10.3390/sym10110588.

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In this study, we apply a robust optimization approach to a p-center facility location problem under uncertainty. Based on a symmetric interval and a multiple allocation strategy, we use three types of uncertainty sets to formulate the robust problem: box uncertainty, ellipsoidal uncertainty, and cardinality-constrained uncertainty. The equivalent robust counterpart models can be solved to optimality using Gurobi. Comprehensive numerical experiments have been conducted by comparing the performance of the different robust models, which illustrate the pattern of robust solutions, and allocating

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