Selected Publications on MFD
- Allwright, J. C. 1980: ``A Feasible Direction Algorithm for
Convex Optimization: Global Convergence Rates'', Journal of Optimization
Theory and Applications , Vol. 30, pp. 1-18
- Belegundu, A. D.; Berke, L.; Patnaik, S. N. 1995: ``An
Optimization Algorithm Based on the Method of Feasible Directions'',
Structural Optimization , Vol. 9, 83-88
- Cawood, M. E.; Kostreva, M. M. 1994: ``Norm-relaxed Method of
Feasible Directions for Solving Nonlinear Programming Problems'', Journal
of Optimization Theory and Applications , Vol. 83, No. 2, 311-320
- Chaney, R. W. 1976: ``On the Pironneau-Polak Method of Centers'',
Journal of Optimization Theory and Applications , Vol. 20, 269-295
- Chaney, R. W. 1976: ``On the Rate of Convergence of Some Feasible
Direction Algorithm'', Journal of Optimization Theory and Applications
, Vol. 20, 297-313
- Chen, X.. 1999: Methods of Feasible Directions for Nonlinear
Programming:Theory and Algorithms , Ph. D. dissertation, Department of Mathematical Sciences,
Clemson University, August, 1999.
- Chen, X.; Kostreva, M. M. 1998: ``Methods for Finding Feasible
Points in Norm-Relaxed Method of Feasible Directions (MFD)'',
the Proceedings of the Fourth International Conference on Optimization:
Techniques and Applications , July 1-3, 1998. Perth, Australia
- Chen, X.; Kostreva, M. M. 1999: ``Global Convergence Analysis
of the Algorithms for Finding Feasible Points in Norm-Relaxed MFD'',
Journal of Optimization Theory and Applications , Vol. 100, No.2,
287-309
- Chen, X.; Kostreva, M. M.1999: ``A Generalization of the
Norm-Relaxed Method of Feasible Directions'', Applied Mathematics and
Computation Vol. 102, No.2-3, 257-272
- Chen, X. and Kostreva, M. M. 1998: ``Methods of Feasible Directions:
A Review'', presented at 1998 Miniconference on Optimization ,
June 29-30, 1998. Univerisity of Western Australia,Perth, Australia and
published in Progress in Optimization, X. Yang et al. (eds.),
Kluwer Academic Press, Norwell, MA, 205-219, May 2000.
- Elwakeil, O. A.; Arora, J. S. 1995: ``Methods for Finding
Feasible Points in Constrained Optimization'', AIAA Journal ,
Vol. 33, No. 9, 1715-1719
- Herskovits, J. N. 1986: ``A Two-Stage Feasible Directions
Algorithm for Nonlinear Constrained Optimization'', Mathematical
Programming , Vol. 36, 19-38
- Herskovits, J.; Santos, G. 1997: ``On the Computer
Implementation of Feasible Direction Interior Point Algorithms for Nonlinear
Optimization'', Structural Optimization , Vol. 14, 165-172
- Korycki, J. A. 1995: Norm-relaxed Method of Feasible
Directions , Ph. D. dissertation, Department of Mathematical Sciences,
Clemson University, August, 1995.
- Korycki, J. A.; Kostreva, M. M. 1996: ``Convergence Analysis
of Norm-relaxed Method of Feasible Directions'', Journal of Optimization
Theory and Applications , Vol. 91, No. 2, 389-418
- Korycki, J. A.; Kostreva, M. M. 1996: ``Norm-relaxed Method
of Feasible Directions: Application in Structural Optimization'',
Structural Optimization , Vol. 11, No. 3/4, 187-194
- Korycki, J. A.; Kostreva, M. M. 1997: ``Self-Tuning
Norm-Relaxed Method of Feasible Directions'', Journal of Optimization
Theory and Applications , Vol. 92, No. 2, 311-330
- Kostreva, M. M. 1989: ``Generalization of Murty's Direct
Algorithm to Linear and Convex Quadratic Programming'', Journal of
Optimization Theory and Applications , Vol. 62, pp. 63-76
- Kostreva, M. M.; Chen, X. B.; Korycki, J. A. 1996: ``A
Norm-Relaxed Method of Feasible Directions for Solving Nonlinear Programming
Problems'', Proceedings of 6th AIAA/USAF/NASA/ISSMO Symposium on
Multidisciplinary Analysis and Optimization , Bellevue, WA, September 1996
- Kostreva, M. M. and Chen, X. 1998: ``A Multi-Directional Method
of Feasible Directions'', presented at International Symposium on
Computational and Optimization Algorithms, Techniques and Applications
(inside of 4th International Conference on Information Systems Analysis
and Synthesis'98) , July 12 - 16, 1998. Orlando, USA
- Kostreva, M. M. and Chen, X.: ``Asymptotic Rates of Convergence of
SQP-Type Methods of Feasible Directions'', in Optimization
Methods and Applications , (Eds. X. Q. Yang, K.L. Teo, and L. Caccetta), Kluwer Academic Publishers,
2001 pp. 247-265.
- Kostreva, M. M. and Chen, X.: ``A Superlinearly Convergent Method of
Feasible Directions'', Applied Mathematics and Computation 116 (2000) pp. 231-244.
- Mayne, D. Q.; Sahba, M. 1985: ``An Efficient Algorithm for
Solving Inequalities'', Journal of Optimization Theory and Applications
, Vol. 45, No. 3, 407-423
- Panier, E. R.; Tits, A. L. 1987: ``A Superlinearly Convergent
Feasible Method for the Solution of Inequality Constrained Optimization
Problems'', SIAM Journal on Control and Optimization , Vol. 25,
No. 4, 934-950
- Panier, E. R.; Tits, A. L.; Herskovits, J. N. 1988: ``A
QP-Free, Globally Convergent, Locally Superlinearly Convergent Algorithm for
Inequality Constrained Optimization'', SIAM Journal on Control and
Optimization , Vol. 26, No. 4, 788-811
- Panier, E. R.; Tits, A. L. 1993: ``On Combining Feasibility,
Descent and Superlinear Convergence in Inequality Constrained Optimization'',
Mathematical Programming , Vol. 59, 261-276
- Pironneau, O.; Polak, E. 1972: ``On the Rate of Convergence
of Certain Methods of Centers'', Mathematical Programming , Vol. 2,
230-257
- Pironneau, O.; Polak, E. 1973: ``Rate of Convergence of a
Class of Methods of Feasible Directions'', SIAM Journal on Numerical
Analysis , Vol. 10, 161-173
- Polak, E. 1971: Computational Methods in Optimization ,
Academic Press, New York
- Polak, E.; Trahan, R.; Mayne, D. Q. 1979: ``Combined Phase I -
Phase II Methods of Feasible Directions'', Mathematical Programming ,
Vol.
17, No. 1, 32-61
- Tits, A. L.; Nye, W. T.; Sangiovanni-Vincentelli, A. L. 1986:
``Enhanced Methods of Feasible Directions for Engineering Design Problems'',
Journal of Optimization Theory and Applications , Vol. 5, No. 1,
475-504
- Topkis, D. M.; Veinott, A. F. 1967: ``On the Convergence of
Some Feasible Direction Algorithms for Nonlinear Programming'', SIAM
Journal on Control , Vol. 5, 268-279
- Vanderplaats, G. N. 1984: Numerical Optimization Techniques
for Engineering Design , McGraw Hill, New York
- Vanderplaats, G. N. 1984: ``Efficient Feasible Directions
Algorithm for Design Synthesis'', AIAA Journal , Vol. 22, 1633-1640
- Vanderplaats, G. N. 1993: DOT/DOC Users Manual ,
Vanderplaats, Miura and Associates
- Wiest, E. J.; Polak, E. 1992: ``A Generalized Quadratic
Programming - Based Phase I - Phase II Method for Inequality Constrained
Optimization'', Journal of Applied Mathematics and Optimization ,
Vol. 26, 223-252
- Zoutendijk, G. 1960: Methods of Feasible Directions , Elsevier
Publishing Company, Amsterdam, Netherlands
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