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.     

Optimality conditions in multiobjective differentiable programming

A theorem stated in Ref. 1 is corrected.     

An evaluation of the use of capillary electrophoresis to monitor trace drug residues following the manufacture of pharmaceuticals

Summary The novel use of capillary electrophoresis to the important and developing area of monitoring possible drug residues on pharmaceutical manufacturing equipment is reported. The CE method is applicable to a wide range of basic drugs with sensitivity as low as 25ng/ml (equivalent to 8×10^–8 M). This sensitivity is equivalent to that obtainable for HPLC for the drugs tested and is obtained by employing a combination of a wider bore capillary with low wavelength UV detection. Preliminary evaluation of the method performance shows acceptable precision, linearity, sensitivity and accuracy. Features of the method compared to HPLC include simplicity, ease of method transfer, reductions in analysis set-up time, and reduced costs of solvents and columns.     

ISO radiation sterilization standards

This presentation provides an overview of the current status of the ISO radiation sterilization standards. The ISO standards are voluntary standards which detail both the validation and routine control of the sterilization process. ISO 11137 was approved in 1994 and published in 1995. When reviewing the standard you will note that less than 20% of the standard is devoted to requirements and the remainder is guidance on how to comply with the requirements.

Future standards developments in radiation sterilization are being focused on providing additional guidance. The guidance that is currently provided in informative annexes of ISO 11137 includes: device/packaging materials, dose setting methods, and dosimeters and dose measurement, currently, there are four Technical Reports being developed to provide additional guidance:

1. 1. AAMI Draft TIR, “Radiation Sterilization Material Qualification”

2. 2. ISO TR 13409-1996, “Sterilization of health care products — Radiation sterilization — Substantiation of 25 kGy as a sterilization dose for small or infrequent production batches”

3. 3. ISO Draft TR, “Sterilization of health care products — Radiation sterilization Selection of a sterilization dose for a single production batch” li]4. ISO Draft TR, “Sterilization of health care products — Radiation sterilization-Product Families, Plans for Sampling and Frequency of Dose Audits.”

     

Critical sets in parametric optimization

We deal with one-parameter families of optimization problems in finite dimensions. The constraints are both of equality and inequality type. The concept of a generalized critical point (g.c. point) is introduced. In particular, every local minimum, Kuhn-Tucker point, and point of Fritz John type is a g.c. point. Under fairly weak (even generic) conditions we study the set consisting of all g.c. points. Due to the parameter, the set is pieced together from one-dimensional manifolds. The points of can be divided into five (characteristic) types. The subset of nondegenerate critical points (first type) is open and dense in (nondegenerate means: strict complementarity, nondegeneracy of the corresponding quadratic form and linear independence of the gradients of binding constraints). A nondegenerate critical point is completely characterized by means of four indices. The change of these indices along is presented. Finally, the Kuhn-Tucker subset of is studied in more detail, in particular in connection with the (failure of the) Mangasarian-Fromowitz constraint qualification.     

Constraint qualifications in quasidifferentiable optimization

The classical linearization procedure for differentiable nonlinear programming problems can be naturally generalized to the quasidifferentiable case. As in the classical case one has to impose so-called constraint qualifications on the constraint functions in order to ensure that optimality of a feasible point implies optimality of the nullvector for the corresponding quasilinearized problem. We present various constraint qualifications in a unified setting, propose a new one, and investigate the relations between these conditions.Supported by DFG Grant Pa 219/5-1.     

Core-generating approximate minimum entropy discretization for rough set feature selection in pattern classification

Rough set feature selection (RSFS) can be used to improve classifier performance. RSFS removes redundant attributes whilst retaining important ones that preserve the classification power of the original dataset. Reducts are feature subsets selected by RSFS. Core is the intersection of all the reducts of a dataset. RSFS can only handle discrete attributes, hence, continuous attributes need to be discretized before being input to RSFS. Discretization determines the core size of a discrete dataset. However, current discretization methods do not consider the core size during discretization. Earlier work has proposed core-generating approximate minimum entropy discretization (C-GAME) algorithm which selects the maximum number of minimum entropy cuts capable of generating a non-empty core within a discrete dataset. The contributions of this paper are as follows: (1) the C-GAME algorithm is improved by adding a new type of constraint to eliminate the possibility that only a single reduct is present in a C-GAME-discrete dataset; (2) performance evaluation of C-GAME in comparison to C4.5, multi-layer perceptrons, RBF networks and k-nearest neighbours classifiers on ten datasets chosen from the UCI Machine Learning Repository; (3) performance evaluation of C-GAME in comparison to Recursive Minimum Entropy Partition (RMEP), Chimerge, Boolean Reasoning and Equal Frequency discretization algorithms on the ten datasets; (4) evaluation of the effects of C-GAME and the other four discretization methods on the sizes of reducts; (5) an upper bound is defined on the total number of reducts within a dataset; (6) the effects of different discretization algorithms on the total number of reducts are analysed; (7) performance analysis of two RSFS algorithms (a genetic algorithm and Johnson’s algorithm).     

带模糊约束的最大流问题

首次提出带模糊约束的最大流问题，并根据网络中的弧容量限制是否带有模糊性，分别建立数学模型，给出求解这两个模型的相应算法和有关实例。     

Geometrical nonlinear analysis of structures using residual variables

The capability of nonlinear analysis methods in tracing the equilibrium path depends on how to return to static status. In this paper, some residual factors existed in the iteration steps are employed. By setting the residual load parameter to zero, minimizing its factor and the residual displacement parameter, three novel constraint equations are obtained. The new formulas are proved by numerical examples. All obtained results illustrate the minimum residual load scheme's robustness in comparison with the cylindrical arc-length algorithm and other previous strategies. Moreover, the capacities of new procedures in tracing the load and displacement limit points are assessed.