## Decomposability in Fixed Point Computation |

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### Contents

DECOMPOSABILITY IN FIXED POINT PROBLEMS | 14 |

AN ALGORITHM FOR COMPUTING FIXED POINTS | 37 |

k THE APPLICATION OF DECOMPOSABILITY TO EQUALITY | 46 |

5 other sections not shown

### Common terms and phrases

algorithm approximate fixed point bd(X Chapter closed proper convex cluster point compact set compute t(x constrained optimization problem continuous functions contraction mapping converges decomposable point Definition developed Dh(x direction of recession Doctor of Philosophy dp(x Dq(x dt(x Eaves equality constraints equicontinuous example feasible point finding a fixed finite number fixed point code fixed point problem fixed point theorem function h g and h Hence hull({x hyperrectangle inequality constraints int(X Let F:Z linear approximate fixed m-simplex matrix inverse Merrill 38 necessary Newton's method nonbasic variables nonempty subset nonlinear nonlinear programming nonnegative number of steps Optimal Objective Value Optimal Solution PL approximation point of f point to set Problem 16 Proof proper convex functions Proposition recession of Q Saigal set map shown simplex Solution and Optimal solves P.U.2 subgradient subset of Rm Suggested Starting Point system of equations triangulation of Rm usable point vertex weakly decomposable y-coordinates yields