Exact Computable Representation of Some Second-Order Cone Constrained Quadratic Programming Problems

Solving the quadratically constrained quadratic programming (QCQP) problem is in general NP-hard. Only a few subclasses of the QCQP problem are known to be polynomial-time solvable. Recently, the QCQP problem with a nonconvex quadratic objective function over one ball and two parallel linear constraints is proven to have an exact computable representation, which reformulates the original problem as a linear semidefinite program with additional linear and second-order This work was generously supported by US Army Research Office Grant (No. W911NF-04-D-0003), by the North Carolina State University Edward P. Fitts Fellowship and by National Natural Science Foundation of China (No. 11171177). It is the policy of the Army Research Office that university personnel do not need to do joint work with ARO personnel in order to receive grants from the Army Research Office. Q. Jin Department of Management Science and Engineering, Zhejiang University, Hangzhou, 310058, China e-mail: [email protected] Y. Tian ( ) School of Business Administration, Southwestern University of Finance and Economics, Chengdu, 611130, China e-mail: [email protected] Z. Deng · S.-C. Fang Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC 27695, USA Z. Deng e-mail: [email protected] S.-C. Fang e-mail: [email protected] W. Xing Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China e-mail: [email protected]