A variable rate refining triangulation.(English)Zbl 0634.90062
A new variable rate refive optimization problems of a special structure. As the corresponding problem of the lower level is always a parametric one theoretic results and solution procedures of parametric optimization form an essential base of this method. However, without convexity there is generally no constructive rule for its practical realization. That is why we here consider a generalized primal decomposition approach applicable also to the non-convex case. We will present a theoretic foundation of this approach and a corresponding solution procedure together with a first local convergence statement.
MSC:
| 90C30 | Nonlinear programming |
| 65H10 | Numerical computation of solutions to systems of equations |
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
Keywords:
fixed points;variable rate refive optimization problems of a special structure. As the corresponding problem of the lower level is always a parametric one theoretic results and solution procedures of parametric optimization;local convergenceCite
Full Text:DOI
References:
| [1] | I. Bárány, ”Subdivisions and triangulations in fixed point algorithms,” International Research Institute for Management Science (Ryleeva, Moscow, U.S.S.R., 1983). |
| [2] | M.N. Broadie, ”Subdivisions and antiprisms for PL homotopy algorithms,” Systems Optimization Laboratory Technical Report No. 83-14, Department of Operations Research, Stanford University (Stanford CA, 1983). |
| [3] | B.C. Eaves, A Course in Triangulations for Solving Equations with Deformations (Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin, 1984). ·Zbl 0558.65035 |
| [4] | B.C. Eaves and R. Saigal, ”Homotopies for the computation of fixed points on unbounded regions,”Mathematical Programming 3 (1972) 225–237. ·Zbl 0258.65060 ·doi:10.1007/BF01584991 |
| [5] | M. Kojima and Y. Yamamoto, ”Variable dimension algorithms: Basic theory, interpretation, and extensions of some existing methods,”Mathematical Programming 24 (1982) 177–215. ·Zbl 0509.90070 ·doi:10.1007/BF01585103 |
| [6] | G. van der Laan and A.J.J. Talman, ”A new subdivision for computing fixed points with a homotopy algorithm,”Mathematical Programming 19 (1980) 78–91. ·Zbl 0438.90104 ·doi:10.1007/BF01581629 |
| [7] | S. Mizuno, ”A simplicial algorithm for finding all solutions to polynomial systems of equations,” Master Thesis, Department of System Sciences, Tokyo Institute of Technology (Tokyo February., 1981). |
| [8] | S. Shamir, ”Two new triangulations for homotopy fixed point algorithms with an arbitrary refinement factor,” in: S.M. Robinson, ed.,Analysis and computation of fixed points (Academic Press, New York, 1980), pp. 25–56. |
| [9] | M.J. Todd, ”On triangulations for computing fixed points,”Mathematical Programming 10 (1976) 322–346. ·Zbl 0358.90047 ·doi:10.1007/BF01580679 |
| [10] | M.J. Todd, ”Union jack triangulations,” in: S. Karamardian and C.B. Garcia, eds,Fixed points: Algorithms and applications (Academic Press, New York, 1977) pp. 315–336. |
| [11] | M.J. Todd, ”Improving the convergence of fixed point algorithms,” in: M.K. Balinski and R.W. Cottle, eds.,Mathematical Programming Study 7 (North-Holland, Amsterdam, 1978) pp. 151–169. ·Zbl 0399.65034 |
| [12] | A.H. Wright, ”The octahedral algorithm, a new simplicial fixed point algorithm,”Mathematical Programming 21 (1981) 47–69. ·Zbl 0475.65029 ·doi:10.1007/BF01584229 |
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