二次规划是非线形规划中一类特殊的数学规划问题，它的解是可以通过求解得到的。通常通过解其库恩—塔克条件（KT条件）,获取一个KT条件的解称为KT对，其中与原问题的变量对应的部分称为KT点。
　　二次规划分为凸二次规划与非凸二次规划，前者的KT点便是其全局极小值点，而后者的KT点可能连局部极小值点都不是。若它的目标函数是二次函数，则约束条件是线性的。由于求解二次规划的方法很多，所以较为复杂；其较简便易行的是沃尔夫法，它是依据库恩－塔克条件，在线性规划单纯形法的基础上加以修正而成的。此外还有莱姆基法、毕尔法、凯勒法等。

• Quadratic programming codes:
  • BQPD from Roger Fletcher
  • CPLEX Barrier/QP solver
  • CPLEX Simplex/QP solver
  • CPLEX Mixed-integer QP solver
  • The Xpress-MP Newton-barrier QP solver from Dash Optimization
  • HOPDM from Jacek Gondzio and Anna Altman
  • LINDO
  • The packages QPC, QPB and QPA from GALAHAD
  • The packages VE02, VE09, VE17, HSL_VE12 and HSL_VE19 from HSL (formerly known as the Harwell Subroutine Library
  • LOQO from Bob Vanderbei
  • MINQ for convex general and non-convex bound constrained problems, in Matlab, by Arnold Neumaier
  • CirCut for finding approximate solutions to certain binary quadratic programs, including the Max-Cut and the Max-Bisection problems, by Yin Zhang
  • The subroutines E04NCF, E04NFF, E04NKF, H02CBF and H02CEF from the NAG fortran library
  • The package nag_qp_sol from the NAG fl90 library
  • The subroutines nag_opt_lin_lsq and nag_opt_sparse_convex_qp from the NAG C library
  • KNITRO from Ziena Optimization Inc. is highly QP-capable.
  • LSSOL from SOL Optimization Software
  • OOQP by Mike Gertz and Steve Wright
  • QPOPT again from SOL Optimization Software
  • The C/Python QP package which is part of CVXOPT
  • The package IQP, by Linda Kaufman and Jessica Hodgins, from the PORT Mathematical Subroutine Library
  • The MOSEK package from Erling and Knud Andersen
  • The subroutine HSQP from John Betts, which is Algorithm 559 from the Collected Algorithms of the ACM
  • The COPL_QP package of Xiong Zhang and Yinyu Ye
  • QuadProg++, a C++ solver for (strictly) convex problems from Luca Di Gaspero
  • The exact solver QP_solver, part of the Computational Geometry Algorithms Library (CGAL)

  See also Hans Mittelmann’s list of QP solvers

   

• Quadratic programming test examples:
  • Maros and Meszaros’s set
  • the same problems within the CUTEr test set
• The latest version of our BiBTeX quadratic programming bibliography.
• A paper summarizing this bibliography (compressed postscript, PDF)
• The overheads from a talk that Nick gave on “Quadratic programming: theory and methods ” at the 3rd FNRS Cycle in Mathematical Programming, Han-sur-Lesse, Belgium, in February 2000.
• The main content of a book on QP by Zhongzhen Zhang

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