# A one-phase interior point method for nonconvex optimization

- Published: 09 Jan 2018

[1] P. R. Amestoy, I. S. Du , and J.-Y. L'Excellent. Mumps multifrontal massively parallel solver version 2.0. 1998.

[2] E. D. Andersen and Y. Ye. A computational study of the homogeneous algorithm for large-scale convex optimization. Computational Optimization and Applications, 10(3):243{269, 1998.

[3] E. D. Andersen and Y. Ye. On a homogeneous algorithm for the monotone complementarity problem. Mathematical Programming, 84(2):375{399, 1999.

[4] H. Y. Benson, D. F. Shanno, and R. J. Vanderbei. Interior-point methods for nonconvex nonlinear programming: jamming and numerical testing. Mathematical programming, 99(1):35{48, 2004.

[5] J. R. Bunch and B. N. Parlett. Direct methods for solving symmetric inde nite systems of linear equations. SIAM Journal on Numerical Analysis, 8(4):639{655, 1971. [OpenAIRE]

[6] R. H. Byrd, J. Nocedal, and R. A. Waltz. Knitro: An integrated package for nonlinear optimization. In Large-scale nonlinear optimization, pages 35{59. Springer, 2006.

[7] L. Chen and D. Goldfarb. Interior-point l2-penalty methods for nonlinear programming with strong global convergence properties. Mathematical Programming, 108(1):1{36, 2006.

[8] F. E. Curtis. A penalty-interior-point algorithm for nonlinear constrained optimization. Mathematical Programming Computation, 4(2):181{209, 2012.

[9] E. D. Dolan and J. J. More. Benchmarking optimization software with performance pro les. Mathematical programming, 91(2):201{213, 2002.

[10] M. Doyle. A barrier algorithm for large nonlinear optimization problems. PhD thesis, Stanford, 2003.

[11] A. V. Fiacco and G. P. McCormick. Nonlinear programming: sequential unconstrained minimization techniques. SIAM, 1990.

[12] R. Fletcher and S. Ley er. Nonlinear programming without a penalty function. Mathematical programming, 91(2):239{269, 2002.

[13] M. Gertz, J. Nocedal, and A. Sartenar. A starting point strategy for nonlinear interior methods. Applied mathematics letters, 17(8):945{952, 2004.

[14] P. E. Gill, M. A. Saunders, and J. R. Shinnerl. On the stability of cholesky factorization for symmetric quaside nite systems. SIAM Journal on Matrix Analysis and Applications, 17(1):35{46, 1996.

[15] P. E. Gill, M. A. Saunders, and E. Wong. On the performance of SQP methods for nonlinear optimization. In Modeling and Optimization: Theory and Applications, pages 95{123. Springer, 2015.

##### Related research

[1] P. R. Amestoy, I. S. Du , and J.-Y. L'Excellent. Mumps multifrontal massively parallel solver version 2.0. 1998.

[2] E. D. Andersen and Y. Ye. A computational study of the homogeneous algorithm for large-scale convex optimization. Computational Optimization and Applications, 10(3):243{269, 1998.

[3] E. D. Andersen and Y. Ye. On a homogeneous algorithm for the monotone complementarity problem. Mathematical Programming, 84(2):375{399, 1999.

[4] H. Y. Benson, D. F. Shanno, and R. J. Vanderbei. Interior-point methods for nonconvex nonlinear programming: jamming and numerical testing. Mathematical programming, 99(1):35{48, 2004.

[5] J. R. Bunch and B. N. Parlett. Direct methods for solving symmetric inde nite systems of linear equations. SIAM Journal on Numerical Analysis, 8(4):639{655, 1971. [OpenAIRE]

[6] R. H. Byrd, J. Nocedal, and R. A. Waltz. Knitro: An integrated package for nonlinear optimization. In Large-scale nonlinear optimization, pages 35{59. Springer, 2006.

[7] L. Chen and D. Goldfarb. Interior-point l2-penalty methods for nonlinear programming with strong global convergence properties. Mathematical Programming, 108(1):1{36, 2006.

[8] F. E. Curtis. A penalty-interior-point algorithm for nonlinear constrained optimization. Mathematical Programming Computation, 4(2):181{209, 2012.

[9] E. D. Dolan and J. J. More. Benchmarking optimization software with performance pro les. Mathematical programming, 91(2):201{213, 2002.

[10] M. Doyle. A barrier algorithm for large nonlinear optimization problems. PhD thesis, Stanford, 2003.

[11] A. V. Fiacco and G. P. McCormick. Nonlinear programming: sequential unconstrained minimization techniques. SIAM, 1990.

[12] R. Fletcher and S. Ley er. Nonlinear programming without a penalty function. Mathematical programming, 91(2):239{269, 2002.

[13] M. Gertz, J. Nocedal, and A. Sartenar. A starting point strategy for nonlinear interior methods. Applied mathematics letters, 17(8):945{952, 2004.

[14] P. E. Gill, M. A. Saunders, and J. R. Shinnerl. On the stability of cholesky factorization for symmetric quaside nite systems. SIAM Journal on Matrix Analysis and Applications, 17(1):35{46, 1996.

[15] P. E. Gill, M. A. Saunders, and E. Wong. On the performance of SQP methods for nonlinear optimization. In Modeling and Optimization: Theory and Applications, pages 95{123. Springer, 2015.