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Journal articles on the topic 'Cardinality constrained optimization'

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Author: Grafiati

Published: 10 March 2023

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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 (April 29, 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 (essentially strongly) stationary point under a suitable problem-tailored quasinormality constraint qualification. Numerical experiments illustrating the performance of the method in comparison to regularization-based approaches are provided.

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2

Bertsimas, Dimitris, and Romy Shioda. "Algorithm for cardinality-constrained quadratic optimization." Computational Optimization and Applications 43, no. 1 (November 15, 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 (July 22, 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 method by proving that it generates limit points satisfying the aforementioned optimality conditions even if the subproblems are only solved inexactly. And we show that, under a suitable Kurdyka–Łojasiewicz-type assumption, any limit point of a standard (safeguarded) multiplier penalty method applied directly to the reformulated problem also satisfies the optimality condition. These results are stronger than corresponding ones known for the related class of mathematical programs with complementarity constraints.

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4

Stephan, Rüdiger. "Cardinality constrained combinatorial optimization: Complexity and polyhedra." Discrete Optimization 7, no. 3 (August 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 (March 6, 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 constrained mean-variance (CCMV) portfolio problem with entropy constraint was found in the literature. This paper introduces modified firefly algorithm (FA) for the CCMV portfolio model with entropy constraint. Firefly algorithm is one of the latest, very successful swarm intelligence algorithm; however, it exhibits some deficiencies when applied to constrained problems. To overcome lack of exploration power during early iterations, we modified the algorithm and tested it on standard portfolio benchmark data sets used in the literature. Our proposed modified firefly algorithm proved to be better than other state-of-the-art algorithms, while introduction of entropy diversity constraint further improved results.

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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 (April 25, 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 (January 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 (June 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 (December 20, 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 optimization problem.

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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

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 (February 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&P indexes.

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14

Monge, Juan F. "Equally weighted cardinality constrained portfolio selection via factor models." Optimization Letters 14, no. 8 (March 17, 2020): 2515–38. http://dx.doi.org/10.1007/s11590-020-01571-6.

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15

Kresta, Aleš. "SOLVING CARDINALITY CONSTRAINED PORTFOLIO OPTIMIZATION PROBLEM BY BINARY PARTICLE SWARM OPTIMIZATION ALGORITHM." Acta academica karviniensia 11, no. 3 (September 30, 2011): 24–33. http://dx.doi.org/10.25142/aak.2011.043.

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16

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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17

Mozafari, Marzieh. "A new IPSO-SA approach for cardinality constrained portfolio optimization." International Journal of Industrial Engineering Computations 2, no. 2 (April 1, 2011): 249–62. http://dx.doi.org/10.5267/j.ijiec.2011.01.004.

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18

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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19

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 (June 2018): 628–42. http://dx.doi.org/10.1016/j.ejor.2017.12.018.

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20

Gao, Jianjun, and Duan Li. "A polynomial case of the cardinality-constrained quadratic optimization problem." Journal of Global Optimization 56, no. 4 (February 1, 2012): 1441–55. http://dx.doi.org/10.1007/s10898-012-9853-z.

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21

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 (July 8, 2021): 493–528. http://dx.doi.org/10.1007/s10898-021-01048-5.

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22

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

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23

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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24

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 (July 10, 2015): 258–71. http://dx.doi.org/10.1080/10556788.2015.1062891.

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25

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 (January 2019): 1211–39. http://dx.doi.org/10.1137/17m1150670.

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26

Jiang, Tao, Shuo Wang, Ruochen Zhang, Lang Qin, Jinglian Wu, Delin Wang, and Selin D. Ahipasaoglu. "An inexact l2-norm penalty method for cardinality constrained portfolio optimization." Engineering Economist 64, no. 3 (July 3, 2019): 289–97. http://dx.doi.org/10.1080/0013791x.2019.1636169.

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27

Murray, Walter, and Howard Shek. "A local relaxation method for the cardinality constrained portfolio optimization problem." Computational Optimization and Applications 53, no. 3 (March 7, 2012): 681–709. http://dx.doi.org/10.1007/s10589-012-9471-1.

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28

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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29

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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30

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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31

Chen, Zhiping, Xinkai Zhuang, and Jia Liu. "A Sustainability-Oriented Enhanced Indexation Model with Regime Switching and Cardinality Constraint." Sustainability 11, no. 15 (July 27, 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 is transformed into a deterministic optimization problem with an ℓ 0 norm constraint. We design a partial penalty method coupled with the proximal alternating direction method of multipliers (ADMM) to solve the deterministic optimization problem. Numerical results in UK and US financial markets confirm the superb performance of the sustainability-oriented RCEI model and the efficiency of the algorithm.

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32

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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33

Lee, Taehan, and Changhyun Kwon. "A short note on the robust combinatorial optimization problems with cardinality constrained uncertainty." 4OR 12, no. 4 (August 8, 2014): 373–78. http://dx.doi.org/10.1007/s10288-014-0270-7.

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34

Boudt, Kris, and Chunlin Wan. "The effect of velocity sparsity on the performance of cardinality constrained particle swarm optimization." Optimization Letters 14, no. 3 (February 13, 2019): 747–58. http://dx.doi.org/10.1007/s11590-019-01398-w.

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35

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 (October 1, 2012): 11–20. http://dx.doi.org/10.1166/asl.2012.3666.

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36

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 (January 9, 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 algorithm (MOEA), which resulted in a competitive solver for continuous unconstrained bi-objective optimization problems. In this paper, we extend the HVN to constrained MOPs with in principle any number of objectives. Similar to the original variant, the first- and second-order derivatives of the involved functions have to be given either analytically or numerically. We demonstrate the applicability of the extended HVN on a set of challenging benchmark problems and show that the new method can be readily applied to solve equality constraints with high precision and to some extent also inequalities. We finally use HVN as a local search engine within an MOEA and show the benefit of this hybrid method on several benchmark problems.

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37

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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38

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 (January 12, 2018): 928–45. http://dx.doi.org/10.1057/s41274-017-0276-6.

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39

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 (April 9, 2008): 577–85. http://dx.doi.org/10.1007/s11590-008-0084-7.

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40

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 (July 9, 2013): 379–97. http://dx.doi.org/10.1007/s10589-013-9582-3.

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41

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 (September 25, 2018): 231–48. http://dx.doi.org/10.24818/18423264/52.3.18.16.

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42

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 (March 2004): 169–204. http://dx.doi.org/10.1023/b:heur.0000026266.07036.da.

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43

Djelassi, Hatim, and Alexander Mitsos. "Global Solution of Semi-infinite Programs with Existence Constraints." Journal of Optimization Theory and Applications 188, no. 3 (February 8, 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 previous work on the global solution of semi-infinite programs (Djelassi and Mitsos in J Glob Optim 68(2):227–253, 2017), we propose (for the first time) an algorithm for the global solution of existence-constrained semi-infinite programs absent any convexity or concavity assumptions. The algorithm is guaranteed to terminate with a globally optimal solution with guaranteed feasibility under assumptions that are similar to the ones made in the regular semi-infinite case. In particular, it is assumed that host sets are compact, defining functions are continuous, an appropriate global nonlinear programming subsolver is used, and that there exists a Slater point with respect to the semi-infinite existence constraints. A proof of finite termination is provided. Numerical results are provided for the solution of an adjustable robust design problem from the chemical engineering literature.

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44

Du, Bo, and Hong Zhou. "A Robust Optimization Approach to the Multiple Allocation p-Center Facility Location Problem." Symmetry 10, no. 11 (November 2, 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 a demand node to multiple facilities can reduce the price of robustness, and reveal that alternative models of uncertainty can provide robust solutions with different conservativeness.

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45

Bucher, Max, and Alexandra Schwartz. "Second-Order Optimality Conditions and Improved Convergence Results for Regularization Methods for Cardinality-Constrained Optimization Problems." Journal of Optimization Theory and Applications 178, no. 2 (June 4, 2018): 383–410. http://dx.doi.org/10.1007/s10957-018-1320-7.

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46

Liagkouras, K., and K. Metaxiotis. "A new efficiently encoded multiobjective algorithm for the solution of the cardinality constrained portfolio optimization problem." Annals of Operations Research 267, no. 1-2 (November 19, 2016): 281–319. http://dx.doi.org/10.1007/s10479-016-2377-z.

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47

Branda, Martin, Max Bucher, Michal Červinka, and Alexandra Schwartz. "Convergence of a Scholtes-type regularization method for cardinality-constrained optimization problems with an application in sparse robust portfolio optimization." Computational Optimization and Applications 70, no. 2 (February 21, 2018): 503–30. http://dx.doi.org/10.1007/s10589-018-9985-2.

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48

Khodamoradi, Tahereh, Maziar Salahi, and Ali Reza Najafi. "A Note on CCMV Portfolio Optimization Model with Short Selling and Risk-neutral Interest Rate." Statistics, Optimization & Information Computing 8, no. 3 (June 14, 2020): 740–48. http://dx.doi.org/10.19139/soic-2310-5070-890.

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In this paper, first we present some drawbacks of the cardinality constrained mean-variance (CCMV) portfolio optimization with short selling and risk-neutral interest rate when the lower and upper bounds of the assets contributions are -1/K and 1/K(K denotes the number of assets in portfolio). Then, we present an improved variant using absolute returns instead of the returns to include short selling in the model. Finally, some numerical results are provided using the data set of the S&P 500 index, Information Technology, and the MIBTEL index in terms of returns and Sharpe ratios to compare the proposed models with those in the literature.

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49

Kizys , Renatas, Angel Juan, Bartosz Sawik, and Laura Calvet . "A Biased-Randomized Iterated Local Search Algorithm for Rich Portfolio Optimization." Applied Sciences 9, no. 17 (August 26, 2019): 3509. http://dx.doi.org/10.3390/app9173509.

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This research develops an original algorithm for rich portfolio optimization (ARPO), considering more realistic constraints than those usually analyzed in the literature. Using a matheuristic framework that combines an iterated local search metaheuristic with quadratic programming, ARPO efficiently deals with complex variants of the mean-variance portfolio optimization problem, including the well-known cardinality and quantity constraints. ARPO proceeds in two steps. First, a feasible initial solution is constructed by allocating portfolio weights according to the individual return rate. Secondly, an iterated local search framework, which makes use of quadratic programming, gradually improves the initial solution throughout an iterative combination of a perturbation stage and a local search stage. According to the experimental results obtained, ARPO is very competitive when compared against existing state-of-the-art approaches, both in terms of the quality of the best solution generated as well as in terms of the computational times required to obtain it. Furthermore, we also show that our algorithm can be used to solve variants of the portfolio optimization problem, in which inputs (individual asset returns, variances and covariances) feature a random component. Notably, the results are similar to the benchmark constrained efficient frontier with deterministic inputs, if variances and covariances of individual asset returns comprise a random component. Finally, a sensitivity analysis has been carried out to test the stability of our algorithm against small variations in the input data.

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50

Liagkouras, K., and K. Metaxiotis. "A new Probe Guided Mutation operator and its application for solving the cardinality constrained portfolio optimization problem." Expert Systems with Applications 41, no. 14 (October 2014): 6274–90. http://dx.doi.org/10.1016/j.eswa.2014.03.051.

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