Novel constraints satisfaction models for optimization problems in container terminals

The growth of containerization and transporting goods in containers has created many problems for ports. In this paper, we systematically survey a literature over problems in container terminals. The operations that take place in container terminals are described and then the problems are classified into five scheduling decisions. For each of the decisions, an overview of the literature is presented. After that, each of the decisions is formulated as Constraint Satisfaction and Optimization Problems (CSOPs). The literature also includes simulations and performance in container terminals. To evaluate any solution methods to the decisions and to measure its efficiency, several indicators are suggested.     

First and second order sensitivity analysis of nonlinear programs under directional constraint qualification conditions

An extension and unification is presented, of the recent results of Shapiro [16] and Gatjvin & Janin [8] about second order differentiability of the optimal value function and directional differentiability of optimal solutions of perturbed mathematical programs, under a relaxed directional version of the Managasarian-Fromowitz constraint qualification condition introduced by Gollan [9]     

Ageing Monitoring of Plastics Used in Nuclear Power Plants by DSC

Degradation of polymeric materials used in nuclear power plants (NPP), especially polymeric cable insulation materials, in the course of their service can be monitored by measuring their properties by DSC, mainly oxidative induction time — OIT. The studied materials were in-laboratory aged by applying main stressors that act in NPP — ionising radiation and temperature. The dependence of OIT on radiation and thermal degradation of polymeric material was determined. The OIT values have been compared to elongation at break as a property that directly reflects the functionality of the studied material. The comparison of monitored OIT of real cable samples taken from NPP with dependencies on how the OIT values change with the elongation at break, makes possible to establish the extent of cable degradation. This method can be considered as a suitable and effective technique for lifetime assessment not only of cable insulations but also of many other plastics. This revised version was published online in July 2006 with corrections to the Cover Date.     

On generalized semi-infinite programming

This paper surveys some basic properties of the class of generalized semi-infinite programming problems (GSIP) where the infinite index set of inequality constraints depends on the state variables and all emerging functions are assumed to be continuously differentiable. There exists a wide range of applications which can be modelled as a (GSIP). The paper discusses extensions of the Mangasarian-Fromovitz, Kuhn-Tucker and Abadie constraint qualification to (GSIP) and presents related first order optimality conditions of Fritz-John and Karush-Kuhn-Tucker type. By using directional differentiability properties of the optimal value function of the lower level problem, first and second order necessary and sufficient optimality conditions are discussed. Several examples illustrate the results presented. The work of this author was supported by CONACYT (México) under grant 44003.     

Weak sharp minima revisited, part II: application to linear regularity and error bounds

The notion of weak sharp minima is an important tool in the analysis of the perturbation behavior of certain classes of optimization problems as well as in the convergence analysis of algorithms designed to solve these problems. It has been studied extensively by several authors. This paper is the second of a series on this subject where the basic results on weak sharp minima in Part I are applied to a number of important problems in convex programming. In Part II we study applications to the linear regularity and bounded linear regularity of a finite collection of convex sets as well as global error bounds in convex programming. We obtain both new results and reproduce several existing results from a fresh perspective. We dedicate this paper to our friend and mentor Terry Rockafellar on the occasion of his 70th birthday. He has been our guide in mathematics as well as in the backcountry and waterways of the Olympic and Cascade mountains. Research supported in part by the National Science Foundation Grant DMS-0203175.     

On existence of weak solutions for one-dimensional forward-backward diffusion equations

We establish the existence of infinitely many weak solutions for the general one-dimensional forward-backward diffusion equation u_t=σ(u_x)_x under the homogeneous Neumann boundary condition by rephrasing it as a first-order differential inclusion problem.     

A Robust SQP Method for Mathematical Programs with Linear Complementarity Constraints

The relationship between the mathematical program with linear complementarity constraints (MPLCC) and its inequality relaxation is studied. Based on this relationship, a new sequential quadratic programming (SQP) method is presented for solving the MPLCC. A certain SQP technique is introduced to deal with the possible infeasibility of quadratic programming subproblems. Global convergence results are derived without assuming the linear independence constraint qualification for MPEC, the nondegeneracy condition, and any feasibility condition of the quadratic programming subproblems. Preliminary numerical results are reported. Research is partially supported by Singapore-MIT Alliance and School of Business, National University of Singapore.     

关于结构KKT方程组的扰动分析

We discuss the perturbation analysis for the structured KKT systems. The methods and results of forward perturbation analysis all differ from the recent works of Gulliksson and other authors. The optimal backward perturbation results can not be deduced by the corresponding results of Sun about the KKT systems.     

Convergence of a Penalty Method for Mathematical Programming with Complementarity Constraints

We adapt the convergence analysis of the smoothing (Ref. 1) and regularization (Ref. 2) methods to a penalty framework for mathematical programs with complementarity constraints (MPCC); we show that the penalty framework shares convergence properties similar to those of these methods. Moreover, we give sufficient conditions for a sequence generated by the penalty framework to be attracted to a B-stationary point of the MPCC.