A combinatorial interior point method for network flow problems

For solving minimum cost flow problems, we develop a combinatorial interior point method based on a variant of the algorithm of Karmarkar, described in Gonzaga [3, 4]. Gonzaga proposes search directions generated by projecting certain directions onto the nullspace ofA. By the special combinatorial structure of networks any projection onto the nullspace ofA can be interpreted as a flow in the incremental graph ofG. In particular, to evaluate the new search direction, it is sufficient to choose a negative circuit subject to costs on the arcs depending on the current solution. That approach results in an O(mn ² L) algorithm wherem denotes the number of vertices,n denotes the number of arcs, andL denotes the total length of the input data.     

SUPPLEMENT TO “PASSAGE, BLOCKADE, SINK AND SOURCE OF A PLANAR DYNAMICAL SYSTEM”

A Theorem is given on the number of passages passing throgh a multiply-connected region,which corrects a wrong conjecture in a former paper of the author.     

Soft Constraint Logic Programming and Generalized Shortest Path Problems

In this paper we study the relationship between Constraint Programming (CP) and Shortest Path (SP) problems. In particular, we show that classical, multicriteria, partially ordered, and modality-based SP problems can be naturally modeled and solved within the Soft Constraint Logic Programming (SCLP) framework, where logic programming is coupled with soft constraints. In this way we provide this large class of SP problems with a high-level and declarative linguistic support whose semantics takes care of both finding the cost of the shortest path(s) and also of actually finding the path(s). On the other hand, some efficient algorithms for certain classes of SP problems can be exploited to provide some classes of SCLP programs with an efficient way to compute their semantics.     

Elliptic problems with discontinuities

In this paper we prove two existence theorems for elliptic problems with discontinuities. The first one is a noncoercive Dirichlet problem and the second one is a Neumann problem. We do not use the method of upper and lower solutions. For Neumann problems we assume that f is nondecreasing. We use the critical point theory for locally Lipschitz functionals.     

Cloud point extraction procedure for flame atomic absorption spectrometric determination of lead(II) in sediment and water samples

The conditions for cloud point extraction of lead(II) from aqueous solutions were investigated and optimized. The procedure is based on the separation of Pb(II) – brillant cresyl blue (BCB) complexes into the micellar media by adding the surfactant Triton X-114. After phase separation, the surfactant-rich phase was dissolved with 1 mol L⁻¹ HNO₃ in ethanol and diluted with 1 mol L⁻¹ HNO₃ solution before lead was determined by flame atomic absorption spectrometry. Optimization of the pH, ligand and surfactant quantities, incubation time, temperature, viscosity, sample volume, and interfering ions was performed. The effects of the matrix ions were also examined. The detection limits for three times the standard deviations of the blank for lead were 7.5 μg L⁻¹ for water samples and 0.33 μg g⁻¹ for sediment samples. The validity of cloud point extraction was checked by employing certified reference samples of Lake Sediment IAEA-SL-1 and Sewage Sludge BCR-CRM 144R. The procedure was applied to natural waters and sediment samples with satisfactory results (recoveries >95%, relative standard deviations <6.4%).     

A Goal Programming model of the reference point method

Real-life decision problems are usually so complex they cannot be modeled with a single objective function, thus creating a need for clear and efficient techniques of handling multiple criteria to support the decision process. The most commonly used technique is Goal Programming. It is clear and appealing, but in the case of multiobjective optimization problems strongly criticized due to its noncompliance with the efficiency (Pareto-optimality) principle. On the other hand, the reference point method, although using similar control parameters as Goal Programming, always generates efficient solutions. In this paper, we show how the reference point method can be modeled within the Goal Programming methodology. It allows us to simplify implementations of the reference point method as well as shows how Goal Programming with relaxation of some traditional assumptions can be extended to a multiobjective optimization technique meeting the efficiency principle.     

拟相似算子近似点谱的连通分支

讨论了Banach空间X上两个算子T，S拟相似时，近似点谱σα(T)的每一个连通分支与σα（S）以及σs(S)的相交关系，证明了σα(T)的每一个连通分支与σs(S)的交非空，并且给出了σα（T）的连通分支与σα（S）交非空的充要条件。     

Local convergence of quasi-Newton methods for B-differentiable equations

We study local convergence of quasi-Newton methods for solving systems of nonlinear equations defined by B-differentiable functions. We extend the classical linear and superlinear convergence results for general quasi-Newton methods as well as for Broyden's method. We also show how Broyden's method may be applied to nonlinear complementarity problems and illustrate its computational performance on two small examples.     

A Derivative-Coderivative Inclusion in Second-Order Nonsmooth Analysis

For twice smooth functions, the symmetry of the matrix of second partial derivatives is automatic and can be seen as the symmetry of the Jacobian matrix of the gradient mapping. For nonsmooth functions, possibly even extended-real-valued, the gradient mapping can be replaced by a subgradient mapping, and generalized second derivative objects can then be introduced through graphical differentiation of this mapping, but the question of what analog of symmetry might persist has remained open. An answer is provided here in terms of a derivative-coderivative inclusion.     

ON THE EXISTENCE THEOREMS OF NONTRIVIAL PERIODIC SOLUTIONS TOA CLASS OF NONLINEAR NON－AUTONOMOUS SYS

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＴＨＥＯＲＥＭＳＯＦＮＯＮＴＲＩＶＩＡＬＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＴＯＡＣＬＡＳＳＯＦＮＯＮＬＩＮＥＡＲＮＯＮ－ＡＵＴＯＮＯＭＯＵＳＳＹＳＴＥＭＳ￥ＧａｏＺｈａｎｈａｉ（高占海）；ＺｈａｎｇＤｉ（张棣）（Ｎｏｒｔｈ...