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Semidefinite Relaxations, Multivariate Normal Distributions, and Order Statistics

  • Dimitris Bertsimas
  • Yinyu Ye
Chapter

Abstract

Given the symmetric matrix \(Q = \left\{ {qij} \right\} \in {R^{n \times n}}\) and the constraint matrix \(A = \left\{ {{a_{ij}}} \right\} \in {R^{m \times n}}\), we consider the quadratic programming (QP) problem with linear and boolean constraints
$$\begin{array}{l} Maximize q\left( x \right): = x'Qx\\ subject to \left| {\sum\limits_{j = 1}^n {{a_{ij}}{x_j}} } \right| = {b_i} = 1,...,m,\\ x_j^2 = 1,j = 1,...,n. \end{array}$$
(QP)
Note that the constraint x j 2 =1 will force x j = 1 or x j = −1, making it a boolean variable.

Keywords

Approximation Algorithm Quadratic Programming Positive Semidefinite Multivariate Normal Distribution Semidefinite Programming 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Dimitris Bertsimas
    • 1
  • Yinyu Ye
    • 2
  1. 1.Sloan School of ManagementMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of Management ScienceThe University of IowaIowa CityUSA

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