On the multiplier rules

We establish new results of first-order necessary conditions of optimality for finite-dimensional problems with inequality constraints and for problems with equality and inequality constraints, in the form of John’s theorem and in the form of Karush–Kuhn–Tucker’s theorem. In comparison with existing results, we weaken assumptions of continuity and of differentiability.     

On alternative theorems and necessary conditions for efficiency

In this article, we establish theorems of the alternative for a system described by inequalities, equalities and a set inclusion, which are generalizations of Tucker's classical theorem of the alternative, and develop Kuhn–Tucker necessary conditions for efficiency to mathematical programs in normed linear spaces involving inequality, equality and set constraints with positive Lagrange multipliers of all the components of objective functions.     

Benson 真有效意义下向量优化的最优性条件

对向量值映射引入了Clarke切导数,A djacent切导数及Contingent导数的概念,讨论了它们的性质,并用其建立了束向量优化有效解在Benson真有效意义下的Fritz John及Kunh-Tucker条件。     

A special complementarity function revisited

ABSTRACT

Recently, a local framework of Newton-type methods for constrained systems of equations has been developed. Applied to the solution of Karush–Kuhn–Tucker (KKT) systems, the framework enables local quadratic convergence under conditions that allow nonisolated and degenerate KKT points. This result is based on a reformulation of the KKT conditions as a constrained piecewise smooth system of equations. It is an open question whether a comparable result can be achieved for other (not piecewise smooth) reformulations. It will be shown that this is possible if the KKT system is reformulated by means of the Fischer–Burmeister complementarity function under conditions that allow degenerate KKT points and nonisolated Lagrange multipliers. To this end, novel constrained Levenberg–Marquardt subproblems are introduced. They allow significantly longer steps for updating the multipliers. Based on this, a convergence rate of at least 1.5 is shown.     

关于双层规划约束规格的一个注记

本文表明了非线性规划中常见的约束规格对一般双层规划不成立,并对双层规划可以满足的较弱的约束规格“部分平静”,给出了使其成立的充分条件．     

Deposition and fabrication of alkanethiolate gold nanocluster films on TiO2(1 1 0) and the effects of plasma etching

Deposition and fabrication of films of Au nanoclusters protected by alkanethiolate ligands are attempted on a TiO₂(1 1 0) surface and the structures of films are observed by a scanning tunneling microscope (STM). Effects of oxygen and hydrogen-plasma etching in addition to UV irradiation on the structure and chemical composition of the films are also investigated by using STM and X-ray photoelectron spectroscopy. Alkanethiolate Au nanoclusters are produced using a modified Brust synthesis method and their LB films are dip-coated on TiO₂(1 1 0). Alkanethiolate Au nanoclusters are weakly bound to the substrate and can be manipulated with an STM tip. Net-like structures of alkanethiolate Au nanoclusters are formed by a strong blast of air. Oxygen-plasma etching removes alkanethiolate ligands and simultaneously oxidizes Au clusters. At room temperature, prolonged oxygen-plasma etching causes agglomeration of Au nanoclusters. UV irradiation removes ligands partly, which makes Au nanoclusters less mobile. The net-like structure of alkanethiolate Au clusters produced by a blast of air is retained after oxygen and hydrogen-plasma etching.     

Validity of the bead-spring model for describing the linear viscoelastic properties of single-strand DNA under strongly denaturing conditions

Using a normal mode analysis, we predict the infinite dilution linear viscoelastic properties of single-strand (ss) DNA molecules and compare the results to the linear viscoelastic data of Shusterman et al. (Phys Rev Let 92(4):048303, 2004) obtained by monitoring the diffusion of a fluorescently labeled terminus of the molecule. To compute the overall best global fit, we constrain the hydrodynamic interaction parameter, h*, equilibrium root mean square spring extension, b, and the number of Kuhn steps per spring, N _K,S, to be equal for the strands compared. The fits using the bead-spring model for all but 23,100 base ss-DNA strands match the experimental data at long times with significant deviations at intermediate and short times. However, parameters fitted separately to all individual strand lengths predict results well. The best fits to data for 2,400 and 6,700 base pairs yield N _K,S ∼12 and h* = 0.12. These values are similar to those found for conventional polymers such as polystyrene which have been successfully modeled with N _K,S ∼7 and h* = 0.15, indicating ss-DNA and polystyrene exhibit analogous hydrodynamic behavior.     

Reference and Incommensurability: What Rigid Designation Won’t Get You

Causal theories of reference in the philosophy of language and philosophy of science have suggested that it could resolve lingering worries about incommensurability between theoretical claims in different paradigms, to borrow Kuhn’s terms. If we co-refer throughout different paradigms, then the problems of incommensurability are greatly diminished, according to causal theorists. I argue that assuring ourselves of that sort of constancy of reference will require comparable sorts of cross-paradigm affinities, and thus provides us with no special relief on this problem. Suggestions on how to think about rigid designation across paradigms are included.