Optimization Toolbox™

Selected Bibliography

[1] Branch, M.A., T.F. Coleman, and Y. Li, "A Subspace, Interior, and Conjugate Gradient Method for Large-Scale Bound-Constrained Minimization Problems," SIAM Journal on Scientific Computing, Vol. 21, Number 1, pp 1-23, 1999.

[2] Byrd, R.H., J. C. Gilbert, and J. Nocedal, "A Trust Region Method Based on Interior Point Techniques for Nonlinear Programming," Mathematical Programming, Vol 89, No. 1, pp. 149–185, 2000.

[3] Byrd, R.H., Mary E. Hribar, and Jorge Nocedal, "An Interior Point Algorithm for Large-Scale Nonlinear Programming, SIAM Journal on Optimization," SIAM Journal on Optimization, Vol 9, No. 4, pp. 877–900, 1999.

[4] Byrd, R.H., R.B. Schnabel, and G.A. Shultz, "Approximate Solution of the Trust Region Problem by Minimization over Two-Dimensional Subspaces," Mathematical Programming, Vol. 40, pp 247-263, 1988.

[5] Coleman, T.F. and Y. Li, "On the Convergence of Reflective Newton Methods for Large-Scale Nonlinear Minimization Subject to Bounds," Mathematical Programming, Vol. 67, Number 2, pp 189-224, 1994.

[6] Coleman, T.F. and Y. Li, "An Interior, Trust Region Approach for Nonlinear Minimization Subject to Bounds," SIAM Journal on Optimization, Vol. 6, pp 418-445, 1996.

[7] Coleman, T.F. and Y. Li, "A Reflective Newton Method for Minimizing a Quadratic Function Subject to Bounds on some of the Variables," SIAM Journal on Optimization, Vol. 6, Number 4, pp 1040-1058, 1996.

[8] Coleman, T.F. and A. Verma, "A Preconditioned Conjugate Gradient Approach to Linear Equality Constrained Minimization," submitted to Computational Optimization and Applications.

[9] Mehrotra, S., "On the Implementation of a Primal-Dual Interior Point Method," SIAM Journal on Optimization, Vol. 2, pp 575-601, 1992.

[10] Moré, J.J. and D.C. Sorensen, "Computing a Trust Region Step," SIAM Journal on Scientific and Statistical Computing, Vol. 3, pp 553-572, 1983.

[11] Sorensen, D.C., "Minimization of a Large Scale Quadratic Function Subject to an Ellipsoidal Constraint," Department of Computational and Applied Mathematics, Rice University, Technical Report TR94-27, 1994.

[12] Steihaug, T., "The Conjugate Gradient Method and Trust Regions in Large Scale Optimization," SIAM Journal on Numerical Analysis, Vol. 20, pp 626-637, 1983.

[13] Waltz, R. A. , J. L. Morales, J. Nocedal, and D. Orban, "An interior algorithm for nonlinear optimization that combines line search and trust region steps," Mathematical Programming, Vol 107, No. 3, pp. 391–408, 2006.

[14] Zhang, Y., "Solving Large-Scale Linear Programs by Interior-Point Methods Under the MATLAB Environment," Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD, Technical Report TR96-01, July, 1995.

Large-Scale Linear Programming

Parallel Computing for Optimization