Trust Region Strategies for Unconstrained and Constrained Minimization |
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algorithm Algorithm 2.1 assume BFGS update Bk+1 bounded CALL DCOPY Chapter COLUMNS COMPF COMPUTE condition number constraints CONTINUE RETURN convergence test CUTLO DDOT DNRM2 DOUBLE PRECISION DTEMP exists f(x+s FUNMIN global convergence GOTO GRADIENT Hessian approximation Hessian matrix IAFLAG INCX inequality INFO INTEGER iteration JPVT L(x,v+Av L2 NORM Lagrange multipliers lemma line search LINPACK MAXIMUM NUMBER MAXNDF Newton step norm NUMDF NXTDLF NXTFUN NXTX obtain orthogonal matrix penalty function permutation matrix PL(x positive definite problem Q-R decomposition q-superlinear convergence QRAUX quadratic approximation quadratic function RADINC radius RETURN END satisfies SIGMA SNORM solution solve SUBROUTINE TEMP theorem triangular matrix trust region trust region strategy unconstrained UPPER TRIANGULAR v+Av v²f(x vector Vf(x Vh(x WORK1 xk+1 ZERO Δν ΔΧ