A unified analysis for a class of long-step primal-dual path-following interior-point algorithms for semidefinite programming

We present a unified analysis for a class of long-step primal-dual path-following algorithms for semidefinite programming whose search directions are obtained through linearization of the symmetrized equation of the central pathH _P (XS) [PXSP ^–1 + (PXSP ^–1) ^T ]/2 = I, introduced by Zhang. At an iterate (X,S), we choose a scaling matrixP from the class of nonsingular matricesP such thatPXSP ^–1 is symmetric. This class of matrices includes the three well-known choices, namely:P = S ^1/2 andP = X ^–1/2 proposed by Monteiro, and the matrixP corresponding to the Nesterov—Todd direction. We show that within the class of algorithms studied in this paper, the one based on the Nesterov—Todd direction has the lowest possible iteration-complexity bound that can provably be derived from our analysis. More specifically, its iteration-complexity bound is of the same order as that of the corresponding long-step primal-dual path-following algorithm for linear programming introduced by Kojima, Mizuno and Yoshise. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.Corresponding author.This author's research is supported in part by the National Science Foundation under grants INT-9600343 and CCR-9700448 and the Office of Naval Research under grant N00014-94-1-0340.This author's research was supported in part by DOE DE-FG02-93ER25171-A001.     

Syntheses and structures of P-anilino-P-chalcogeno- and P-anilino-P-iminodiazasilaphosphetidines and their group 12 and 13 metal compounds

The P-anilino-P-chalcogeno(imino)diazasilaphosphetidines [Me(2)Si(mu-N(t)Bu)(2)P=E(NHPh)] (E = O (3), S (4), Se (5), N-p-tolyl (6)) were synthesized by oxidizing the P-anilinodiazasilaphosphetidine [Me(2)Si(N(t)Bu)(2)P(NHPh)] (2) with cumene hydroperoxide, sulfur, selenium, and p-tolyl azide, respectively. The lithium salt of 4 reacted with thallium monochloride to produce ([Me(2)Si(mu-N(t)Bu)(2)P=S(NPh)-kappaN-kappaS]Tl)(7), which features a two-coordinate thallium atom. Treatment of 4-6 with AlMe(3) gave the monoligand dimethylaluminum complexes ([Me(2)Si(mu-N(t)Bu)(2)P=E(NPh)-kappaN-kappaE]AlMe(2)) (E = S (8), Se (9), N-p-tolyl (10)), respectively. In these complexes the aluminum atom is tetrahedrally coordinated by one chelating ligand and two methyl groups, as a single-crystal X-ray analysis of 8 showed. A 2 equiv amount of 4-6 reacted with diethylzinc to produce the homoleptic diligand complexes ([Me(2)Si(mu-N(t)Bu)(2)P=E(NPh)-kappaN-kappaE](2)Zn)(E = S (11), Se (12), N-p-tolyl (13)). A crystal-structure analysis of 11 revealed a linear tetraspirocycle with a tetrahedrally coordinated, central zinc atom.     

Wetting of InP by indium- and indium-tin melts

Orientation dependent wetting of InP substrates by In- and In_xSn_1−x melts saturated with InP was studied using the sessile drop method. The contact angle was found to depend on the substrate orientation as follows: It is shown that a tin admixture to the indium melt improves the wetting behaviour. Additional to the dependence on substrate orientation it was found an anisotropic wetting on all investigated faces.