QPSchur
swMATH ID:  6918 
Software Authors:  Bartlett, Roscoe A.; Biegler, Lorenz T. 
Description:  QPSchur: A dual, activeset, Schurcomplement method for largescale and structured convex quadratic programming. We describe an activeset, dualfeasible Schurcomplement method for quadratic programming (QP) with positive definite Hessians. The formulation of the QP being solved is general and flexible, and is appropriate for many different application areas. Moreover, the specialized structure of the QP is abstracted away behind a fixed KKT matrix called \(K_{o}\) and other problem matrices, which naturally leads to an objectoriented software implementation. Updates to the working set of active inequality constraints are facilitated using a dense Schur complement, which we expect to remain small. Here, the dual Schur complement method requires the projected Hessian to be positive definite for every working set considered by the algorithm. Therefore, this method is not appropriate for all QPs. While the Schur complement approach to linear algebra is very flexible with respect to allowing exploitation of problem structure, it is not as numerically stable as approaches using a QR factorization. However, we show that the use of fixedprecision iterative refinement helps to dramatically improve the numerical stability of this Schur complement algorithm. The use of the objectoriented QP solver implementation is demonstrated on two different application areas with specializations in each area; largescale model predictive control (MPC) and reducedspace successive quadratic programming (with several different representations for the reduced Hessian). These results demonstrate that the QP solver can exploit applicationspecific structure in a computationally efficient and fairly robust manner as compared to other QP solver implementations. 
Homepage:  https://rd.springer.com/article/10.1007/s110810066588z 
Keywords:  quadratic programming; Schur complement; activeset; dual space; object oriented programming 
Related Software:  qpOASES; LOQO; QPOPT; ZQPCVX; MA57; OSQP; OOQP; CUTEst; NETLIB LP Test Set; GALAHAD; Ipopt; HPIPM; GitHub; fast_mpc; ACADO; HSL_MA97; CPLEX; BPMPD; DEVEX; SQOPT 
Cited in:  17 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

QPSchur: A dual, activeset, Schurcomplement method for largescale and structured convex quadratic programming. Zbl 1167.90615 Bartlett, Roscoe A.; Biegler, Lorenz T. 
2006

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Cited by 34 Authors
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Cited in 11 Serials
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