On a new stochastic global optimization algorithm based on censored observations

In this paper a new algorithm is proposed for global optimization problems. The main idea is that of modifying a standard clustering approach by sequentially sampling the objective function while adaptively deciding an appropriate sample size. Theoretical as well as computational results are presented.     

PERIODIC BOUNDARY VALUE PROBLEM FOR SECOND ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

This paper investigates the periodic boundary value problems for a class of second order functional differential equations. The monotone iterative technique and the maximum principle are applied to obtain the existence of maximal and minimal solutions.     

Partially Strictly Monotone and Nonlinear Penalty Functions for Constrained Mathematical Programs

We introduce the concept of partially strictly monotone functions and apply it to construct a class of nonlinear penalty functions for a constrained optimization problem. This class of nonlinear penalty functions includes some (nonlinear) penalty functions currently used in the literature as special cases. Assuming that the perturbation function is lower semi-continuous, we prove that the sequence of optimal values of nonlinear penalty problems converges to that of the original constrained optimization problem. First-order and second-order necessary optimality conditions of nonlinear penalty problems are derived by converting the optimality of penalty problems into that of a smooth constrained vector optimization problem. This approach allows for a concise derivation of optimality conditions of nonlinear penalty problems. Finally, we prove that each limit point of the second-order stationary points of the nonlinear penalty problems is a second-order stationary point of the original constrained optimization problem.     

含k-次增生算子的Ishikawa迭代的收敛性问题

主要研究了非线性方程x Tx=f的Ishikawa迭代解．其中T为k-次增生的或增生的，并在一致光滑和任意的实Banach空间分别研究了上述方程的带误差的Ishikawa迭代解，从而推广了已知的一些结果。     

Non-compact generalized variational inequalities for quasi-monotone and hemi-continuous operators with applications

Some results are obtained for non-compact cases in topological vector spaces for the existence problem of solutions for some set-valued variational inequalities with quasi-monotone and lower hemi-continuous operators, and with quasi-semi-monotone and upper hemi-continuous operators. Some applications are given in non-reflexive Banach spaces for these existence problems of solutions and for perturbation problems for these set-valued variational inequalities with quasi-monotone and quasi-semi-monotone operators. This revised version was published online in June 2006 with corrections to the Cover Date.     

Algorithms for Finite and Semi-Infinite Min–Max–Min Problems Using Adaptive Smoothing Techniques

We develop two implementable algorithms, the first for the solution of finite and the second for the solution of semi-infinite min-max-min problems. A smoothing technique (together with discretization for the semi-infinite case) is used to construct a sequence of approximating finite min-max problems, which are solved with increasing precision. The smoothing and discretization approximations are initially coarse, but are made progressively finer as the number of iterations is increased. This reduces the potential ill-conditioning due to high smoothing precision parameter values and computational cost due to high levels of discretization. The behavior of the algorithms is illustrated with three semi-infinite numerical examples.     

A new proof for Rockafellar's characterization of maximal monotone operators

We provide a new and short proof for Rockafellar's characterization of maximal monotone operators in reflexive Banach spaces based on S. Fitzpatrick's function and a technique used by R. S. Burachik and B. F. Svaiter for proving their result on the representation of a maximal monotone operator by convex functions.

     

Recent developments in the characterisation of microemulsions

Microemulsions are becoming increasingly complex systems by containing more sophisticated surfactants, polymers, biomolecules, inorganic nanoparticles, etc. The detailed understanding of such more complex systems requires increasingly more refined and comprehensive characterisation. This is typically done by the combination of complementary techniques and is aided by the fact that several experimental methods have been improved (such as electron microscopy) in recent times, new ones have become available (such as fluorescence correlation spectroscopy), and the theoretical understanding of structural data is advancing.     

A structured light-based system for human heads

The 3-D modeling of heads by using optical triangulation techniques is of great interest in the context of virtual reality, telecommunication and computer animation. This paper presents a structured light-based system mainly for human heads. It is named “3-D Laser Color Scanner” (3DLCS). A 3-D model is obtained with a cylindrical scan. The laser beam is switched on and off using a “light valve” and two successive CCD frames are captured, one with the laser line showing and one without. We can simplify the laser line extracting by subtracting these two images.In this system, two CCD cameras are used to avoid occlusion problems. Color information is read from the CCD when the laser light is absent. Since traditional laser scanner will miss the range data in the low-reflectance areas such as the hair area of human head, a shape from silhouette algorithm is presented to overcome this problem. Finally, we give some results using our system. The resulting model is suitable for many applications.     

Iterative Schemes for Nonconvex Variational Inequalities

In this paper, we suggest and analyze some iterative methods for solving nonconvex variational inequalities using the auxiliary principle technique, the convergence of which requires either only pseudomonotonicity or partially relaxed strong monotonicity. Our proofs of convergence are very simple. As special cases, we obtain earlier results for solving general variational inequalities involving convex sets.