Optimal mechanism design using interior-point methods

Mechanism and Machine Theory

Volumn 35, Issue 1, 2000, Pages 83-98

  Zhang, Xiong ^a   Zhou, Ji ^a   Ye, Yingyu ^b  

^a HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b UNIVERSITY OF IOWA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CONSTRAINT THEORY; FUNCTIONS; ITERATIVE METHODS; MACHINE DESIGN; NONLINEAR PROGRAMMING;

INTERIOR-POINT METHODS; PRIMAL-DUAL INTERIOR POINT ALGORITHMS;

MECHANISMS;

EID: 0033742829     PISSN: 0094114X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0094-114X(99)00003-8     Document Type: Article

References (29)

1. Fox R.L., Gupta K.C. Optimization technology as applied to mechanisms design. ASME Journal of Engineering for Industry. 95:1973;657-663.
2. Paradis M.J., Willmert K.D. Optimal mechanism design using the Gauss constrained method. ASME Journal of Mechanical Design. 104:1982;1-10.
3. Rosen J.B. The gradient projection method for nonlinear programming. Part I: linear constraints. Journal of the Society for Industrial and Applied Mathematics. 8:1960;181-217.
4. Sohoni V.N., Haug E.J. A state space technique for optimal design of mechanisms. Progress in Engineering Optimization. 1981;39-47 ASME, New York.
5. Fallahi B., Hall A.S., Ragsdell K.M. Application of the generalized reduced gradient method to selected mechanism synthesis problems. Progress in Engineering Optimization. 1981;49-56 ASME, New York.
6. Wilde D.J. Error linearization in the least-squares design of function generating mechanisms. Progress in Engineering Optimization. 1981;33-37 ASME, New York.
7. Chen F.Y., Chan V-L. Synthesis of function generating mechanisms using Marquardt's method. ASME Journal of Engineering for Industry. 96:1974;131-137.
8. Sutherland G.H., Roth R. An improved least squares method for designing function generating mechanisms. ASME Journal of Engineering for Industry. 97:1975;303-307.
9. Ye Y. Recovering the optimal dual solutions in Karmarkar's polynomial algorithm for linear programming. Mathematical Programming. 39:1987;305-317.
10. Y. Ye, O. Guler, R.A. Tapia, Y. Zhang, A quadratically convergent O( nL )-iteration algorithm for linear programming. Technical report TR91-26, Department of Mathematical Sciences, Rice University, Houston, TX, 1991.
11. Ye Y., Anstreicher K. On quadratic and O ( nL ) convergence of predictor-corrector algorithm for LCP. Mathematical Programming. 62:1993;537-552.
12. 3L) primal-dual potential reduction algorithm for solving convex quadratic programs. Mathematical Programming. 61:1993;161-170.
13. Monteiro R.C., Adler I. Interior path following primal-dual algorithms. Part II: convex quadratic programming. Mathematical Programming. 44:1989;43-66.
14. Zhu J. A path following algorithm for a class of convex programming problems. ZOR-Methods and Models of Operations Research. 36:1992;359-377.
15. Kortanek K.O., Potra F., Ye Y. On some efficient interior point methods for nonlinear convex programming. Linear Algebra and its Applications. 152:1991;169-198.
16. Karmarkar N. A new polynomial time algorithm for linear programming. Combinatorica. 4:1984;373-395.
17. Kojima M., Megiddo N., Mizuno S. A primal-dual infeasible-interior-point algorithm for linear programming. Mathematical Programming. 61:1993;263-280.
18. Lustig I.J., Marsten R.E., Shanno D.F. On implementing Mehrotra's predictor-corrector interior point method for linear programming. SIAM Journal on Optimization. 2:1992;435-449.
19. Lustig I.J., Marsten R.E., Shanno D.F. Computational experience with a primal-dual interior-point method for linear programming. Linear Algebra and its Applications. 152:1991;191-222.
20. McShane K.A., Monma C.L., Shanno D. An implementation of a primal-dual interior point method for linear programming. ORSA Journal on Computing. 1:1989;70-83.
21. Mehrotra S. On the implementation of a primal-dual interior point. SIAM Journal on Optimization. 2:1992;575-601.
22. X. Zhang, Interior-point methods for engineering optimization and its applications. Ph.D. Thesis, Huazhong University of Science and Technology, 1995, pp. 8-20.
23. Monteiro R.D.C. A global convergent primal-dual interior point algorithm for convex programming. Mathematical Programming. 64:1994;123-147.
24. Zhang Y., Zhang D. Superlinear convergence of infeasible-interior-point methods for linear programming. Mathematical Programming. 66:1994;361-377.
25. F.A. Potra, A quadratically convergent infeasible interior-point algorithm for linear programming. Report no. 28, Department of Mathematics, The University of Iowa, IA, 1992.
26. Mizuno S. Polynomiality of infeasible-interior-point algorithms for linear programming. Mathematical Programming. 67:1994;109-119.
27. Fletcher R. Practical Methods of Optimzation. 1987;Wiley, New York.
28. Schittkowski K. The nonlinear programming method of Wilson, Han and Powell with an augmented Lagrangian type line search function, Part I: convergence analysis. Numerical Mathematics. 38:1981;83-114.
29. B.A. Murtagh, M.A. Saunders, MINOS 1.5 user's guide. Technical report SOL 83-20R, Systems Optimization Laboratory, Department of Operations Research, Stanford University, CA, 1987.