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Table 1: Comparison of the hessians
Table I. Differentiable problems. Lipschitz constants and global solutions.
Table II. Non-differentiable problems. Lipschitz constants and global solutions.
Table 2: Change in the condition numbers of the Hessian matrix and the preconditioned Hessian matrix
2000
"... In PAGE 18: ...ax.eig.X`S` = the maximum eigenvalue of X`S`: From the numerical results in Table 1, we observe that all the variants could generate only low accuracy approximate optimal solutions; we need more sophisticated implementation to compute higher accuracy optimal solutions. Table2 shows how the condition number of r2g(yk; k), the condition number of Lkr2g(yk; k)(Lk)T , where Lk(Lk)T denotes the Cholesky factorization of the quasi-Newton BFGS matrix Hk (see Section 3.3), and # CG, the number of iterations in CG method in the predictor procedure changed along the sequence f(yk; k)g generated the BFGS + 2nd-order version applied to the SDP relaxation of the BQIP with n = 100 (the last column of Table 1) .... ..."
Cited by 4
Table 1: Test set statistics. Number of variables, number of integer variables, number of con- straints, number of non zero entries in the Hessian of the Lagrangian, optimal solution value and value of the continuous relaxation are listed. (The optimum for trimloss5 is not known.)
2005
Table 4: Comparison among the LP methods on Min-Var and Lipschitz condition objectives. Notation: Min-
"... In PAGE 6: ... Of course, #0Cnding smoothness objectives that result in smaller LPs is a direction for future work. The performances of the new LP formulations with #5Csmooth- ness quot; objectives are studied in Table4 . We use the coe#0E- cients #280.... ..."
Table 7 Modi ed Hessians with trust region
1994
"... In PAGE 16: ... The measure of distance to feasibility (the {tube strategy), the nonmonotone updating of penalty parameter d, and the trust region strategy were essentially dormant during the solution process regardless of the iterates apos; proximity to the solution or to feasibility. In fact, the only evidence of our enhancements on the small number of CUTE test problems that we solved occurred when d was decreased slightly while solving the problem MANNE employing modi ed Hessians with a trust region strategy (see the third and fourth rows of Table7 ). It is noteworthy that the iterates that resulted from solving this problem with the penalty parameter arti cially held xed at d = 1 were identical to iterates that resulted for the adjusted d solution.... ..."
Cited by 27
Table 1: CPU times for the Hessian and gradient.
2000
"... In PAGE 4: ... For comparison, one iteration of a barrier method applied to the primal problem (5) would have a complexity of at least O(n6) ops, since we have O(n2) variables. 5 Numerical Results Table1 lists CPU times required for evaluation of the gradient and Hessian of (z) as a function of problem size. Notice the jump in CPU time that results when the problem size crosses a power of two.... ..."
Cited by 2
Table 1: CPU times for the Hessian and gradient.
"... In PAGE 4: ... For comparison, one iteration of a barrier method applied to the primal problem #285#29 would have a complexity of at least O#28n 6 #29 #0Dops, since wehave O#28n 2 #29variables. 5 Numerical Results Table1 lists CPU times required for evaluation of the gradient and Hessian of #1E#28z#29 as a function of problem size. Notice the jump in CPU time that results when the problem size crosses a power of two.... ..."
Table 2 Modi ed Hessians with no trust region
1994
Cited by 27
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