New global algorithms for quadratic programming with a few negative eigenvalues based on alternative direction method and convex relaxation

Luo, Hezhi; Bai, Xiaodi; Lim, Gino J.; Peng, Jiming

doi:10.1007/s12532-018-0142-9

Cited by 25 publications

(20 citation statements)

References 45 publications

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“…As pointed out in Luo et al (2019), although there exist many other strong relaxation models for QCQP, they usually involve more intensive computation. In this work, we combine the relaxation model ( 13) with other simple optimization techniques to develop a global algorithm for Problem ( P ).…”

Section: The Quadratic Convex Relaxationmentioning

confidence: 99%

“…In this subsection, we present a global algorithm (called SCOBB) for Problem ( P ) that integrates the SCO approach with the B&B framework based on the quadratic convex relaxation (13) and the adaptive branch-and-cut rule from Luo et al (2019). The SCOBB algorithm for Problem ( P ) is described in Algorithm 2.…”

Section: The Scobb Algorithmmentioning

confidence: 99%

“…(ii) Based on the special structure of the relaxation (13), we adopt the adaptive branch-and-cut rule from Luo et al (2019) to cut off the optimal solution to the relaxation problem corresponding…”

Section: End Whilementioning

confidence: 99%

“…to the node with the smallest lower bound after each iteration, so that the lower bound will be improved (see Figure 1 for an illustration in Luo et al (2019)).…”

Section: End Whilementioning

confidence: 99%

See 3 more Smart Citations

Effective Algorithms for Optimal Portfolio Deleveraging Problem with Cross Impact

Luo¹,

Chen²,

Zhang³

et al. 2020

Preprint

Self Cite

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Section: The Quadratic Convex Relaxationmentioning

confidence: 99%

Section: The Scobb Algorithmmentioning

confidence: 99%

Section: End Whilementioning

confidence: 99%

“…to the node with the smallest lower bound after each iteration, so that the lower bound will be improved (see Figure 1 for an illustration in Luo et al (2019)).…”

Section: End Whilementioning

confidence: 99%

See 2 more Smart Citations

Effective Algorithms for Optimal Portfolio Deleveraging Problem with Cross Impact

Luo¹,

Chen²,

Zhang³

et al. 2020

Preprint

Self Cite

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“…Vandenbussche (2008, 2009) and Chen and Burer (2012) propose the B&B algorithms for nonconvex quadratic programs with linear and/or box constraints by using semi-definite relaxations of the first-order KKT conditions of the problem with finite KKTbranching. More recently, Luo et al (2019) develop a new global algorithm for a nonconvex quadratic program with linear and convex quadratic constraints by combining several simple optimization techniques such as the alternative direction method, the B&B framework and the convex relaxation. This approach is further extended to the worst-case linear optimization with uncertainties that arises in estimating the systemic risk in financial systems (cf.…”

Section: Introductionmentioning

confidence: 99%

Effective algorithms for optimal portfolio deleveraging problem with cross impact

Luo

Chen

Zhang

et al. 2023

Mathematical Finance

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We investigate the optimal portfolio deleveraging (OPD) problem with permanent and temporary price impacts, where the objective is to maximize equity while meeting a prescribed debt/equity requirement. We take the real situation with cross impact among different assets into consideration. The resulting problem is, however, a nonconvex quadratic program with a quadratic constraint and a box constraint, which is known to be NP‐hard. In this paper, we first develop a successive convex optimization (SCO) approach for solving the OPD problem and show that the SCO algorithm converges to a KKT point of its transformed problem. Second, we propose an effective global algorithm for the OPD problem, which integrates the SCO method, simple convex relaxation, and a branch‐and‐bound framework, to identify a global optimal solution to the OPD problem within a prespecified ε‐tolerance. We establish the global convergence of our algorithm and estimate its complexity. We also conduct numerical experiments to demonstrate the effectiveness of our proposed algorithms with both real data and randomly generated medium‐ and large‐scale OPD instances.

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A novel branch‐and‐bound algorithm for solving linear multiplicative programming problems

Hu,

Gu,

Wang

2024

Optim Control Appl Methods

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This article proposes a rectangular branch‐and‐bound algorithm for solving linear multiplication problems (LMP) globally. In order to obtain a reliable lower bound of the original problem, this article designs a novel linear relaxation programming problem (LRP) that has not been seen in the existing literature. Based on the basic framework of the rectangular branch and bound algorithm, this article proposes an algorithm that can obtain a global solution. According to the structure of linear relaxation programming, the article designs a region reduction technology to improve the efficiency of the algorithm. This article also provides convergence analysis to ensure the reliability of the algorithm. Finally, several numerical experiments are used to demonstrate the effectiveness and robustness of the algorithm.

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New global algorithms for quadratic programming with a few negative eigenvalues based on alternative direction method and convex relaxation

Cited by 25 publications

References 45 publications

Effective Algorithms for Optimal Portfolio Deleveraging Problem with Cross Impact

Effective Algorithms for Optimal Portfolio Deleveraging Problem with Cross Impact

Effective algorithms for optimal portfolio deleveraging problem with cross impact

A novel branch‐and‐bound algorithm for solving linear multiplicative programming problems

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