Convex relaxations and MIQCQP reformulations for a class of cardinality-constrained portfolio selection problems

Cui, Xueting; Zheng, Xue; Zhu, Shushang; Sun, Xiao

doi:10.1007/s10898-012-9842-2

Cited by 69 publications

(59 citation statements)

References 27 publications

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“…Unlike other existing branch-and-bound methods in the literature where standard quadratic programming relaxation is adopted as the bounding technique, Shaw et al (2008) used Lagrangian relaxation with cost splitting to generate a lower bound at each node of the binary search tree and employed subgradient method to compute the Lagrangian bound. Cui et al (2013) investigated a class of cardinality constrained portfolio selection problems with different risk measures and tracking error control. Utilizing the natural decomposition of factor models, a second-order cone program relaxation and an MIQCQP reformulation were derived in Cui et al (2013) for this class of problems.…”

Section: Problem and Backgroundmentioning

confidence: 99%

“…Cui et al (2013) investigated a class of cardinality constrained portfolio selection problems with different risk measures and tracking error control. Utilizing the natural decomposition of factor models, a second-order cone program relaxation and an MIQCQP reformulation were derived in Cui et al (2013) for this class of problems. Recently, a novel geometric approach is proposed in Gao and Li (2013) for minimizing a quadratic function subject to a cardinality constraint.…”

Section: Problem and Backgroundmentioning

confidence: 99%

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

Zheng

Sun

2014

INFORMS Journal on Computing

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We consider in this paper quadratic programming problems with cardinality and minimum threshold constraints which arise naturally in various real-world applications such as portfolio selection and subset selection in regression. This class of problems can be formulated as mixed-integer 0-1 quadratic programs. We propose a new semidefinite program (SDP) approach for computing the "best" diagonal decomposition that gives the tightest continuous relaxation of the perspective reformulation of the problem. We also give an alternative way of deriving the perspective reformulation by applying a special Lagrangian decomposition scheme to the diagonal decomposition of the problem. This derivation can be viewed as a "dual" method to the convexification method employing the perspective function on semi-continuous variables. Computational results show that the proposed SDP approach can be advantageous for improving the performance of MIQP solvers when applied to the perspective reformulations of the problem.

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Section: Problem and Backgroundmentioning

confidence: 99%

Section: Problem and Backgroundmentioning

confidence: 99%

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

Zheng

Sun

2014

INFORMS Journal on Computing

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“…where α(u, η, µ, σ) and β(v, η, µ, σ, λ, π) are defined by (17) and (18), respectively. Consequently, the problem in (20)- (22) can be expressed as…”

Section: Lift-and-convexification Approachmentioning

confidence: 99%

“…For instance, in production planning, the semi-continuous variables are used to describe the state of a production process that is either turned off (inactive), hence nothing is produced, or turned on (active) such that the production level has to lie in certain interval ( [22,26,27]). Other typical applications of semi-continuous variables include portfolio selection with minimum buy-in threshold ( [35,21,17,45]) and lot-sizing with minimum order quantity ( [3,41]). …”

Section: Introductionmentioning

confidence: 99%

“…Portfolio selection problems with cardinality and/or minimum threshold constraints have been studied extensively in recent literature. For exact solution methods, please see, e.g., [7,37,44,13,6,17,29]. For inexact solution methods, such as heuristics, local search methods and randomized techniques, please see, e.g., [34,12,15,35,43,38,16,40,19,46].…”

Section: Introductionmentioning

confidence: 99%

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Quadratic Convex Reformulations for Semicontinuous Quadratic Programming

Wu¹,

Sun²,

Li³

2017

SIAM J. Optim.

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We consider in this paper a class of semi-continuous quadratic programming problems which arises in many real-world applications such as production planning, portfolio selection and subset selection in regression. We propose a lift-and-convexification approach to derive an equivalent reformulation of the original problem. This liftand-convexification approach lifts the quadratic term involving x only in the original objective function f (x, y) to a quadratic function of both x and y and convexifies this equivalent objective function. While the continuous relaxation of our new reformulation attains the same tight bound as achieved by the continuous relaxation of the well known perspective reformulation, the new reformulation also retains the linearly constrained quadratic programming structure of the original mix-integer problem. This prominent feature improves the performance of branch-and-bound algorithms by providing the same tightness at the root node as the state-of-the-art perspective reformulation and offering much faster processing time at children nodes. We further combine the liftand-convexification approach and the quadratic convex reformulation approach in the literature to form an even tighter reformulation. Promising results from our computational tests in both portfolio selection and subset selection problems numerically verify the benefits from these theoretical features of our new reformulations.

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Concentrated portfolio selection models based on historical data

Chen

Wang

2014

Appl Stoch Models Bus & Ind

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A new risk measure fully based on historical data is proposed, from which we can naturally derive concentrated optimal portfolios rather than imposing cardinality constraints. The new risk measure can be expressed as a quadratics of the introduced greedy matrix, which takes investors' joint behavior into account. We construct distribution‐free portfolio selection models in simple case and realistic case, respectively. The latest techniques for describing transaction cost constraints and solving nonconvex quadratic programs are utilized to obtain the optimal portfolio efficiently. In order to show the practicality, efficiency, and robustness of our new risk measure and corresponding portfolio selection models, a series of empirical studies are carried out with trading data from advanced stock markets and emerging stock markets. Different performance indicators are adopted to comprehensively compare results obtained under our new models with those obtained under the mean‐variance, mean‐semivariance, and mean‐conditional value‐at‐risk models. Out‐of‐sample results sufficiently show that our models outperform the others and provide a simple and practical approach for choosing concentrated, efficient, and robust portfolios. Copyright © 2014 John Wiley & Sons, Ltd.

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Convex relaxations and MIQCQP reformulations for a class of cardinality-constrained portfolio selection problems

Cited by 69 publications

References 27 publications

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

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

Quadratic Convex Reformulations for Semicontinuous Quadratic Programming

Concentrated portfolio selection models based on historical data

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