现代物流技术中装卸工问题的拟多项式时间可解情况

装卸工问题是从现代物流技术中提出的一个实际问题，这个问题的雏形早在上个世纪60年代中国科学院数学研究所就提出和研究过。现代物流业的迅速发展，促成和推动装卸工问题的提出和研究。装卸工问题是一个新的NP困难的组合优化问题，本文研究限制情形下的装卸工问题，并证明是拟多项式时间可解的。     

Two-Parameter Asymptotics in a Boundary-Value Problem for the Laplacian

We study a model boundary-value problem for the Laplacian in the unit disk with closely-spaced and periodic alternation of the type of boundary condition for the case in which the Dirichlet problem is the limit one. We study and justify the two-parameter asymptotics of an eigenvalue of the perturbed problem converging to a simple eigenvalue of the limit problem.     

Eigenvibrations of a bar with elastically attached load

We study the problem on the eigenvibrations of a bar with an elastically attached load. The problem is reduced to finding the eigenvalues and eigenfunctions of an ordinary secondorder differential problem with a spectral parameter nonlinearly occurring in the boundary condition at the load attachment point. We prove the existence of countably many simple positive eigenvalues of the differential problem. The problem is approximated by a grid scheme of the finite element method. We study the convergence and accuracy of the approximate solutions.     

On the Existence of a Generalized Solution of the Saturated-Unsaturated Filtration Problem

We study the existence of a generalized solution of an initial–boundary value problem describing the process of unsteady filtration of a liquid in a bounded region of an n-dimensional space. We consider the case in which the Kirchhoff transformation used to determine the generalized solution takes the real axis into a semiaxis bounded below. An auxiliary problem is constructed. It is proved that any solution of the auxiliary problem is a solution of the problem under study. The solvability of the auxiliary problem is established by using the method of semidiscretization in time and the Galerkin method.     

Algorithms for the computation of functionals defined on the solution of a discrete ill-posed problem

We study a linear, discrete ill-posed problem, by which we mean a very ill-conditioned linear least squares problem. In particular we consider the case when one is primarily interested in computing a functional defined on the solution rather than the solution itself. In order to alleviate the ill-conditioning we require the norm of the solution to be smaller than a given constant. Thus we are lead to minimizing a linear functional subject to two quadratic constraints. We study existence and uniqueness for this problem and show that it is essentially equivalent to a least squares problem with a linear and a quadratic constraint, which is easier to handle computationally. Efficient algorithms are suggested for this problem.     

On a non-homogeneous eigenvalue problem involving a potential: An Orlicz–Sobolev space setting

In this paper we study a non-homogeneous eigenvalue problem involving variable growth conditions and a potential V. The problem is analyzed in the context of Orlicz–Sobolev spaces. Connected with this problem we also study the optimization problem for the particular eigenvalue given by the infimum of the Rayleigh quotient associated to the problem with respect to the potential V when V lies in a bounded, closed and convex subset of a certain variable exponent Lebesgue space.     

A study of mixed discrete bilevel programs using semidefinite and semi-infinite programming

In this paper, we study the bilevel programming problem with discrete polynomial lower level problem. We start by transforming the problem into a bilevel problem comprising a semidefinite program (SDP for short) in the lower level problem. Then, we are able to deduce some conditions of existence of solutions for the original problem. After that, we again change the bilevel problem with SDP in the lower level problem into a semi-infinite program. With the aid of the exchange technique, for simple bilevel programs, an algorithm for computing a global optimal solution is suggested, the convergence is shown, and a numerical example is given.     

A pricing problem under Monge property

We study a pricing problem where buyers with non-uniform demand purchase one of many items. Each buyer has a known benefit for each item and purchases the item that gives the largest utility, which is defined to be the difference between the benefit and the price of the item. The optimization problem is to decide on the prices that maximize total revenue of the seller. This problem is also called the optimal product line design problem in the absence of competition.

Even though the general problem is known to be NP-hard, it can be solved efficiently under some natural assumptions on customer benefits. In this paper we study properties of optimal solutions and present a dynamic programming algorithm when customer benefits satisfy the Monge property. The same algorithm can also be used to solve the problem under the additional requirement that all buyers should be served.     

Global Method for Monotone Variational Inequality Problems with Inequality Constraints

We consider optimization methods for monotone variational inequality problems with nonlinear inequality constraints. First, we study the mixed complementarity problem based on the original problem. Then, a merit function for the mixed complementarity problem is proposed, and some desirable properties of the merit function are obtained. Through the merit function, the original variational inequality problem is reformulated as simple bounded minimization. Under certain assumptions, we show that any stationary point of the optimization problem is a solution of the problem considered. Finally, we propose a descent method for the variational inequality problem and prove its global convergence.     

Solving semi-infinite programs by smoothing projected gradient method

In this paper, we study a semi-infinite programming (SIP) problem with a convex set constraint. Using the value function of the lower level problem, we reformulate SIP problem as a nonsmooth optimization problem. Using the theory of nonsmooth Lagrange multiplier rules and Danskin’s theorem, we present constraint qualifications and necessary optimality conditions. We propose a new numerical method for solving the problem. The novelty of our numerical method is to use the integral entropy function to approximate the value function and then solve SIP by the smoothing projected gradient method. Moreover we study the relationships between the approximating problems and the original SIP problem. We derive error bounds between the integral entropy function and the value function, and between locally optimal solutions of the smoothing problem and those for the original problem. Using certain second order sufficient conditions, we derive some estimates for locally optimal solutions of problem. Numerical experiments show that the algorithm is efficient for solving SIP.     

Dynamic optimization of the operation of single-car elevator systems with destination hall call registration: Part I. Formulation and simulations

The purpose of this two-part study is to investigate the operation problem of single-car elevator systems with destination hall call registration. Destination hall call registration is such a system in which passengers register their destination floors at elevator halls before boarding the car, while in the ordinary systems passengers specify only the directions of their destination floors at elevator halls and register destination floors after boarding the car. In this part of the study, we formulate the operation problem as a dynamic optimization problem and demonstrate by computer simulations that dynamically optimized operation considerably improves the transportation capability compared to conventional selective collective operation. How to solve the dynamic optimization problem is given in the second part of this study.     

Invariant sets and symmetric periodic motions of reversible mechanical systems

A method of constructing and classifying all symmetric periodic motions of a reversible mechanical system is proposed. The principal solution of the above problem is given for the Hill problem, the restricted three-body problem (including the photogravitational problem), the problem of a heavy rigid body with a fixed point, and that of a heavy rigid body on a rough plane. In particular, problems requiring a systematic numerical study are therby formulated.     

A Note on a Two-dimensional Dynamic Programming Problem

A two-dimensional dynamic programming problem is posed. By relaxing some of the restraints on the problem it is reduced to a standard dynamic programming problem. Results are quoted from a particular case study.     

A location-routing problem in glass recycling

In this study, a location-routing problem encountered in glass recycling is addressed. We formulate a combined maximal covering location problem in the presence of partial coverage and selective traveling salesman problem to determine the location of bottle banks and the route of a collecting vehicle that will daily visit a number of customers and the bottle banks. We propose a nested heuristic procedure to solve the problem. The outer loop of the heuristic is based on variable neighborhood search while the inner loop solves the traveling salesman problem on the locations defined. The performance of the heuristic procedure is demonstrated with computational experimentation on instances that are both randomly generated and are taken from the literature. An application of the procedure on a case study using a geographical information system is also reported.     

Problem on small motions and normal oscillations of capillary viscous liquids in rotating vessels

The new recent results of the author are applied to study the problem. We begin from the problem posing. Then we consider the problem as a system of operator equations in a Hilbert space. Further, the initial-boundary value problem is reduced to the Cauchy problem for the abstract parabolic equation; this allows us to prove the unique solvability theorem. Then we study normal oscillations of the hydraulic system under the assumption of static stability with respect to the linear approximation. We prove results about the spectrum of the problem and prove that the system of root functions (eigenfunctions and associated functions) form a basis. Also, we prove that if the static stability assumption is not satisfied, then the inversion of Lagrange’s theorem on the stability is valid.     

MERIT FUNCTION AND GLOBAL ALGORITHM FOR BOX CONSTRAINED VARIATIONAL INEQUALITIES

1 IntroductionWe consider tlie variational inequality problelll, deuoted by VIP(X, F), wliicli is to find avector x* E X such thatF(X*)"(X -- X-) 2 0, VX E X, (1)where F: R" - R" is any vector-valued f11uction and X is a uonelllpty subset of R'.This problem has important applicatiolls. in equilibriun1 modeIs arising in fields such asecououtics, transportatioll scieuce alld operations research. See [1]. There exist mauy lllethodsfor solviug tlie variational li1equality problem VIP(X. …     

Study of a Numerical Approach for a Transient Flow Problem in Porous Media

In this work, we deal with the numerical study of the new approximation method proposed in [7] for a transient flow problem in porous media. The stationary problem, obtained from a time discretization of this transient problem, is considered as an optimal shape design formulation. We prove the existence of the solution of the discrete optimal shape problem obtained from finite element discretization. We study the convergence and give numerical results showing the efficiency of the proposed approach.     

Mixed Elastico-Plasticity Problems with Partially Unknown Boundaries

In this paper,we study mixed elastico-plasticity problems in which part of the boundary is known,while the other part of the boundary is unknown and is a free boundary.Under certain conditions,this problemcan be transformed into a Riemann-Hilbert boundary value problem for analytic functions and a mixed boundaryvalue problem for complex equations.Using the theory of generalized analytic functions,the solvability of theproblem is discussed.     

限制情况下装卸工问题的最优解

装卸工问题是从现代物流技术中提出的一个实际问题,这个问题的雏形早在上个世纪60年代中国科学院数学研究所就提出和研究过.现代物流技术迅速发展,促成和推动装卸工问题的提出和研究.装卸工问题是一个新的NP困难的组合优化问题,首先介绍装卸工问题及限制情况下装卸工问题的数学模型,然后分析限制情况下的装卸工问题的性质,最后给出该问题的所有最优解.     

Complexity and approximation results for the connected vertex cover problem in graphs and hypergraphs

We study a variation of the vertex cover problem where it is required that the graph induced by the vertex cover is connected. We prove that this problem is polynomial in chordal graphs, has a PTAS in planar graphs, is APX-hard in bipartite graphs and is 5/3-approximable in any class of graphs where the vertex cover problem is polynomial (in particular in bipartite graphs). Finally, dealing with hypergraphs, we study the complexity and the approximability of two natural generalizations.