Improving the Performance of MIQP Solvers for Quadratic Programs with Cardinality and Minimum Threshold Constraints: A Semidefinite Program Approach

Published Online:https://doi.org/10.1287/ijoc.2014.0592

References

  • Aktürk M, Atamtürk A, Gürel Set al. (2009) A strong conic quadratic reformulation for machine-job assignment with controllable processing times. Oper. Res. Lett. 37:187–191.CrossrefGoogle Scholar
  • Arthanari TS, Dodge Y (1993) Mathematical Programming in Statistics (John Wiley & Sons, New York).Google Scholar
  • Ben-Tal A, Nemirovski AS (2001) Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, MPS-SIAM Series on Optimization (Society for Industrial Mathematics, Philadelphia).CrossrefGoogle Scholar
  • Bertsimas D, Shioda R (2009) Algorithm for cardinality-constrained quadratic optimization. Comput. Optimi. Appl. 43:1–22.CrossrefGoogle Scholar
  • Bienstock D (1996) Computational study of a family of mixed-integer quadratic programming problems. Math. Program. 74:121–140.CrossrefGoogle Scholar
  • Blog B, van der Hoek G, Rinnooy Kan AHG, Timmer GT (1983) The optimal selection of small portfolios. Management Sci. 29:792–798.LinkGoogle Scholar
  • Bonami P, Lejeune MA (2009) An exact solution approach for portfolio optimization problems under stochastic and integer constraints. Oper. Res. 57:650–670.LinkGoogle Scholar
  • Breiman L (1995) Better subset regression using the nonnegative garrote. Technometrics 37:373–384.CrossrefGoogle Scholar
  • Cesarone F, Scozzari A, Tardella F (2009) Efficient algorithms for mean-variance portfolio optimization with hard real-world constraints. Giornale dell'Istituto Italiano degli Attuari 72:37–56.Google Scholar
  • Chang TJ, Meade N, Beasley JE, Sharaiha YM (2000) Heuristics for cardinality constrained portfolio optimisation. Comput. Oper. Res. 27:1271–1302.CrossrefGoogle Scholar
  • Cui XT, Zheng XJ, Zhu SS, Sun XL (2013) Convex relaxations and MIQCQP reformulations for a class of cardinality-constrained portfolio selection problems. J. Global Optim. 56:1409–1423.CrossrefGoogle Scholar
  • Frangioni A, Gentile C (2006) Perspective cuts for a class of convex 0-1 mixed integer programs. Math. Program. 106:225–236.CrossrefGoogle Scholar
  • Frangioni A, Gentile C (2007) SDP diagonalizations and perspective cuts for a class of nonseparable MIQP. Oper. Res. Lett. 35:181–185.CrossrefGoogle Scholar
  • Frangioni A, Gentile C (2009) A computational comparison of reformulations of the perspective relaxation: SOCP vs. cutting planes. Oper. Res. Lett. 37:206–210.CrossrefGoogle Scholar
  • Gao JJ, Li D (2013) Optimal cardinality constrained portfolio selection. Oper. Res. 61:745–761.LinkGoogle Scholar
  • Grant M, Boyd S (2009) CVX: MATLAB software for disciplined convex programming, http://cvxr.com/cvx/download/.Google Scholar
  • Guignard M, Kim S (1987) Lagrangean decomposition: A model yielding stronger Lagrangean bounds. Math. Program. 39:215–228.CrossrefGoogle Scholar
  • Günlük O, Linderoth J (2010) Perspective reformulations of mixed integer nonlinear programs with indicator variables. Math. Program. 124:183–205.CrossrefGoogle Scholar
  • Hiriart-Urruty JB, Lemaréchal C (1993) Convex Analysis and Minimization Algorithms: Fundamentals (Springer Verlag, New York).CrossrefGoogle Scholar
  • Jacob NL (1974) A limited-diversification portfolio selection model for the small investor. J. Finance 29:847–856.CrossrefGoogle Scholar
  • Jobst NJ, Horniman MD, Lucas CA, Mitra G (2001) Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints. Quant. Finance 1:489–501.CrossrefGoogle Scholar
  • Li D, Sun XL, Wang J (2006) Optimal lot solution to cardinality constrained mean-variance formulation for portfolio selection. Math. Finance 16:83–101.CrossrefGoogle Scholar
  • Maringer D, Kellerer H (2003) Optimization of cardinality constrained portfolios with a hybrid local search algorithm. OR Spectrum 25:481–495.CrossrefGoogle Scholar
  • Michelon P, Maculan N (1991) Lagrangian decomposition for integer nonlinear programming with linear constraints. Math. Program. 52:303–313.CrossrefGoogle Scholar
  • Miller AJ (2002) Subset Selection in Regression, Second ed. (Chapman and Hall, London).CrossrefGoogle Scholar
  • Mitra G, Ellison F, Scowcroft A (2007) Quadratic programming for portfolio planning: Insights into algorithmic and computational issues. Part ii: Processing of portfolio planning models with discrete constraints. J. Asset Management 8:249–258.CrossrefGoogle Scholar
  • Pólik I, Terlaky T (2007) A survey of the 𝒮-lemma. SIAM Rev. 49:371–418.CrossrefGoogle Scholar
  • Shaw DX, Liu S, Kopman L (2008) Lagrangian relaxation procedure for cardinality-constrained portfolio optimization. Optim. Methods Software 23:411–420.CrossrefGoogle Scholar
  • Tawarmalani M, Sahinidis NV (2001) Semidefinite relaxations of fractional programs via novel convexification techniques. J. Global Optim. 20:133–154.CrossrefGoogle Scholar
  • Vandenberghe L, Boyd S (1996) Semidefinite programming. SIAM Rev. 38:49–95.CrossrefGoogle Scholar
  • Xie J, He S, Zhang S (2008) Randomized portfolio selection, with constraints. Pacific J. Optim. 4:89–112.Google Scholar
  • Yuan M, Lin Y (2007) On the non-negative garrotte estimator. J. Roy. Statist. Soc. Ser. B 69:143–161.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.