Hybrid Approach with Active Set Identification for Mathematical Programs with Complementarity Constraints

We consider a mathematical program with complementarity constraints (MPCC). Our purpose is to develop methods that enable us to compute a solution or a point with some kind of stationarity to MPCC by solving a finite number of nonlinear programs. We apply an active set identification technique to a smoothing continuation method (Ref. 1) and propose a hybrid algorithm for solving MPCC. We develop also two modifications: one makes use of an index addition strategy; the other adopts an index subtraction strategy. We show that, under reasonable assumptions, all the proposed algorithms possess a finite termination property. Further discussions and numerical experience are given as well This work was supported in part by the Scientific Research Grant-in-Aid from the Ministry of Education, Science, Sports, and Culture of Japan. The authors are grateful to Professor Paul Tseng for helpful suggestions on an earlier version of the paper.     

Liquid chromatographic determination of dimethadione and trimethadione in human serum on octadecyl treated microporous glass columns

Summary The liquid chromatographic determination of trimethadione (TMO) and its methabolite, dimethadione (DMO) were studied by high-performance liquid chromatography (HPLC) on octadecyl-modified microporous glasses, prepared with toluene solution containing octadecyl-dimethylchlorosilane, using two types of microporous glass with various mean pore diameters and/or specific surface areas. Using acetonitrile-water mixtures as eluents, TMO and DMO in human serum were separated on the glasses studied, but with different degrees of resolution. In this present study, we report the development of a rapid and selective HPLC method for the simultaneous analysis of TMO and DMO in human serum.     

A Modified Relaxation Scheme for Mathematical Programs with Complementarity Constraints

In this paper, we consider a mathematical program with complementarity constraints. We present a modified relaxed program for this problem, which involves less constraints than the relaxation scheme studied by Scholtes (2000). We show that the linear independence constraint qualification holds for the new relaxed problem under some mild conditions. We also consider a limiting behavior of the relaxed problem. We prove that any accumulation point of stationary points of the relaxed problems is C-stationary to the original problem under the MPEC linear independence constraint qualification and, if the Hessian matrices of the Lagrangian functions of the relaxed problems are uniformly bounded below on the corresponding tangent space, it is M-stationary. We also obtain some sufficient conditions of B-stationarity for a feasible point of the original problem. In particular, some conditions described by the eigenvalues of the Hessian matrices mentioned above are new and can be verified easily. This work was supported in part by the Scientific Research Grant-in-Aid from the Ministry of Education, Science, Sports, and Culture of Japan. The authors are grateful to an anonymous referee for critical comments.     

Application of the alternating direction method of multipliers to separable convex programming problems

This paper presents a decomposition algorithm for solving convex programming problems with separable structure. The algorithm is obtained through application of the alternating direction method of multipliers to the dual of the convex programming problem to be solved. In particular, the algorithm reduces to the ordinary method of multipliers when the problem is regarded as nonseparable. Under the assumption that both primal and dual problems have at least one solution and the solution set of the primal problem is bounded, global convergence of the algorithm is established.     

Site-specific valence-band X-ray photoelectron spectra of a SrTiO3 single-crystal by X-ray standing wave technique

Site-specific valence-band X-ray photoelectron spectra of SrTiO₃ (111) were successfully obtained by using X-ray standing wave technique. Contributions of the Ti and SrO₃ derived states to the valence-band spectra were clearly separated. The spectra provided not only site-specific but also bulk-sensitive information on the SrTiO₃ crystal because of the use of a high-energy synchrotron X-ray source (hν=4750 eV) for photoelectron excitation with the large escape depth. The electronic structures calculated by the DV-Xα method using a (Sr₈Ti₂₇O₁₀₈)⁹²⁻ cluster model well reproduced the observed structures in the valence-band spectra. The partial density of states of both Ti and Sr ions in SrTiO₃ were mainly distributed over the bottom of the valence-band to produce the covalent bonding with O ions.     

Photoinduced one-electron reduction of MV2+ in titania nanosheets using porphyrin in mesoporous silica thin films

Composite films of a meso-(tetramethylpyridinium)porphyrin (TMPyP) hybrid incorporated in mesoporous silica (MPS) and cast on a methyl viologen (MV2+)/titania nanosheet hybrid were synthesized and a light-induced charge separation between the two could be observed. These composite thin films were able to initiate a one-electron reduction of the MV2+ ions accompanied by the simultaneous decomposition of the TMPyP organic dye within the mesoporous silica channels.