亚热带高原湖泊水质方程一类自由初边值问题

亚热带高原湖泊除了有来自工业、农业，生活污水及落尘的外部污染，还有来自湖泊藻类水生生物循环及底泥的污染物释放内污染源污染。因此，由于进出水量不均衡性导致湖水边界的自由变动。本文首先运用微元分析法导出在外源和内源双重污染下湖泊水质模型，然后对一类自由初边值问题通过对非柱形边界条件的齐次约化，运用变分型算子的向量扩张和拟单调方法获得解的存在性、唯一性。     

Inventory control as a discrete system control for the fixed-order quantity system

This paper shows how to model a problem to find optimal number of replenishments in the fixed-order quantity system as a basic problem of optimal control of the discrete system. The decision environment is deterministic and the time horizon is finite. A discrete system consists of the law of dynamics, control domain and performance criterion. It is primarily a simulation model of the inventory dynamics, but the performance criterion enables various order strategies to be compared. The dynamics of state variables depends on the inflow and outflow rates. This paper explicitly defines flow regulators for the four patterns of the inventory: discrete inflow – continuous/discrete outflow and continuous inflow – continuous/discrete outflow. It has been discussed how to use suggested model for variants of the fixed-order quantity system as the scenarios of the model. To find the optimal process, the simulation-based optimization is used.     

Risk-sensitive and risk-neutral control for continuous-time hidden Markov models

In this paper the optimal control of a continuous-time hidden Markov model is discussed. The risk-sensitive problem involves a cost function which has an exponential form and a risk parameter, and is solved by defining an appropriate information state and dynamic programming. As the risk parameter tends to zero, the classical risk-neutral optimal control problem is recovered. The limits are proved using viscosity solution methods.The first author wishes to acknowledge the funding of the activities of the Cooperative Research Centre for Robust and Adaptive Systems by the Australian Commonwealth Government under the Cooperative Research Centers Program. The support of NSERC Grant A7964 is acknowledged by the second author, as is the hospitality of the Department of Systems Engineering and the Cooperative Research Centre for Robust and Adaptive Systems, Australian National University, in July 1993.     

Bootstrapped confidence bands for percentile lifetime

Summary We propose bootstrapped confidence bands for the percentile lifetime function. Our method is based on a joint approximation of the empirical and quantile processes and their bootstrapped counterparts. Modest simulations support the results. Confidence bands are applied to quantile and median residual lifetimes of tractor rear brakes. Research done while at Carleton University Norman Paterson Centre: also partially supported by NSERC Canada grants of M. Cs?rgő. Research supported in part by a NSERC Canada operating grant. Research done while at Carleton University; also partially supported by NSERC Canada grants of m. Cs?rgő and D. A. Dawson and by an EMR Canada grant of M. Cs?gő. Research supported in part by a United States Department of Agriculture CSRS grant and a United States NSF grant of D. M. Bates, G. Wahba and B. S. Yandell.     

Equilibria for networks with malicious users

We consider the problem of characterizing user equilibria and optimal solutions for selfish routing in a given network. We extend the known models by considering malicious behavior. While selfish users follow a strategy that minimizes their individual cost, a malicious user will use his flow through the network in an effort to cause the maximum possible damage to the overall cost. We define a generalized model, present characterizations of flows at equilibrium and prove bounds for the ratio of the social cost of a flow at equilibrium over the cost when centralized coordination among users is allowed. An extended abstract of this work appeared in the Proceedings of the 14th Annual International Symposium on Algorithms and Computation (ISAAC) 2003. G. Karakostas’ research was supported by an NSERC Discovery research grant and MITACS. Part of this research was done when Viglas was a postdoctoral fellow at the University of Toronto, Canada.     

Relaxation methods for monotropic programs

We propose a dual descent method for the problem of minimizing a convex, possibly nondifferentiable, separable cost subject to linear constraints. The method has properties reminiscent of the Gauss-Seidel method in numerical analysis and uses the-complementary slackness mechanism introduced in Bertsekas, Hosein and Tseng (1987) to ensure finite convergence to near optimality. As special cases we obtain the methods in Bertsekas, Hosein and Tseng (1987) for network flow programs and the methods in Tseng and Bertsekas (1987) for linear programs.Work supported by the National Science Foundation under grant NSF-ECS-8519058 and by the Army Research Office under grant DAAL03-86-K-0171.This author is also supported by Canadian NSERC under Grant U0505.     

A two parameter mixed interior-exterior penalty algorithm

In this paper, we analyze the mixed penalty methods introduced in the classic book of Fiacco and McCormick usingtwo distinct penalty parametersr, t. The two penalty coefficients induce a two-parameter differentiable trajectory. We analyze the numerical behaviour of an extrapolation strategy that follows the path of the two-parameter trajectory. We show also how to remove the ill-conditioning by suitable transformations of the equations. In the resulting theory, we show that function values as well as distances to the optimum are both governed by the same behaviour as interior methods (two-step superlinearly convergent, with limiting exponent 4/3).Research partially supported by NSERC grant OGP0036512.Research partially supported by NSERC grant OGP0005491.     

Variational Methods in Convex Analysis

We use variational methods to provide a concise development of a number of basic results in convex and functional analysis. This illuminates the parallels between convex analysis and smooth subdifferential theory. Research was supported by NSERC and by the Canada Research Chair Program and National Science Foundation under grant DMS 0102496.     

Optimization methods in a nonhomogeneous periodic stochastic control model

A discrete-time stochastic optimal control model is considered. The traditional model assumes that all objects are homogeneous in time. However, in many applications some objects are time-dependent. In general, the optimization problem is apparently unsolvable in a nonhomogeneous model with an unbounded time horizon. If the transition function and the utility function are constrained to satisfy a natural periodicity condition, then the nonhomogeneous problem reduces to a homogeneous problem and becomes fully solvable. The objective of this study is to develop and generalize these results to a general constructive paradigm, which produces solution methods for both nonhomogeneous and homogeneous stochastic optimal control problems. The study has been partially supported by the Russian Foundation of Basic Research, grant No. 95-01-01137. Translated from Nelineinye Dinamicheskie Sistemy: Kachestvennyi Analiz i Upravlenie — Sbornik Trudov, No. 2, pp. 20–35, 1994.     

How to compute least infeasible flows

It is well-known how to use maximum flow to decide when a flow problem with demands, lower bounds, and upper bounds is infeasible. Less well-known is how to compute a flow that is least infeasible. This paper considers many possible ways to define “least infeasible” and shows how to compute optimal flows for each definition. For each definition it also gives a dual characterization in terms of cuts, a polynomial routine for recognizing that type of least infeasible flow, and relates that definition to dual cut canceling min-cost flow network algorithms. This research was partially supported by an NSERC Operating Grant, an NSERC Grant for Research Abroad, and a UBC Killam Faculty Study Leave Fellowship. Parts of this research were done while the author was visiting Laboratoire ARTEMIS IMAG at Université Joseph Fourier de Grenoble, France.     

STOCHASTIC MODEL OF LAKE SYSTEM INVASION AND ITS OPTIMAL CONTROL: NEURODYNAMIC PROGRAMMING AS A SOLUTION METHOD

Abstract We develop a stochastic model for the process of spread of an aquatic invader in a lake system. The invader is transported along with recreation boats, and treatment of boats allows one to control the invader spread. Optimization of invasion and control costs leads to a dynamic programming problem. However, standard stochastic dynamic programming (SDP) algorithms allow us to solve the problem for at most 13–14 lakes, which is significantly less than the size of systems arising in applications. We have developed a new technique, which is based upon the ideas of reinforcement learning and neurodynamic programming. This approach allows us to obtain approximate but reasonable control policy for essentially greater lake systems. The resulting numerical technique is comparatively easy to implement, and it can be applied to other spatially extended optimal control problems as well.     

Geometry of homogeneous convex cones,duality mapping,and optimal self-concordant barriers

We study homogeneous convex cones. We first characterize the extreme rays of such cones in the context of their primal construction (due to Vinberg) and also in the context of their dual construction (due to Rothaus). Then, using these results, we prove that every homogeneous cone is facially exposed. We provide an alternative proof of a result of Güler and Tunç el that the Siegel rank of a symmetric cone is equal to its Carathéodory number. Our proof does not use the Jordan-von Neumann-Wigner characterization of the symmetric cones but it easily follows from the primal construction of the homogeneous cones and our results on the geometry of homogeneous cones in primal and dual forms. We study optimal self-concordant barriers in this context. We briefly discuss the duality mapping in the context of automorphisms of convex cones and prove, using numerical integration, that the duality mapping is not an involution on certain self-dual cones.Research of this author was supported in part by a Summer Undergraduate Research Assistantship Award from NSERC (Summer 2001) and a research grant from NSERC while she was an undergraduate student at Faculty of Mathematics, University of Waterloo.Research of this author was supported in part by a PREA from Ontario, Canada and research grants from NSERC. Corresponding author.Mathematics Subject Classification (2000): 90C25, 90C51, 90C60, 90C05, 65Y20, 52A41, 49M37, 90C30     

An explication of secret sharing schemes

This paper is an explication of secret sharing schemes, emphasizing combinatorial construction methods. The main problem we consider is the construction of perfect secret sharing schemes, for specified access structures, with the maximum possible information rate.In this paper, we present numerous direct constructions for secret sharing schemes, such as the Shamir threshold scheme, the Boolean circuit construction of Benaloh and Leichter (for general access structures), the vector space construction of Brickell, and the Simmons geometric construction. We discuss the connections between ideal schemes (i.e., those with information rate equal to one) and matroids. We also mention the entropy bounds of Capocelli et al. Then we give a very general construciton, called the decomposition construction, and numerous applications of it. In particular, we study schemes for access structures based on graphs and the many interesting bounds that can be proved; and we determine the exact value of the optimal information rate for all access structures on at most four participants.Research supported by NSERC (Canada) grant A9287.     

A note on the existence of subgradients

We describe an apparently novel way of constructing the subgradient of a convex function defined on a finite dimensional vector space.Research partially funded on NSERC grant A5116.     

Local analytic invariants and splitting theorems in differential analysis

We show that several classical problems concerning the splitting of exact sequences of spaces of differentiable functions can be reduced to questions of semicontinuity of discrete local invariants in analytic geometry. We thus provide a uniform approach to the continuous linear solution of the division, composition and extension problems in differential analysis, recovering the classical theorems and giving many new results. Dedicated to the memory of David P. Milman Research partially supported by NSERC operating grant A9070. Supported by NSERC University Research Fellowship and operating grant A8849.     

The multiple server center location problem

In this paper, we introduce the multiple server center location problem. p servers are to be located at nodes of a network. Demand for services of these servers is located at each node, and a subset of nodes are to be chosen to locate one or more servers in each. Each customer selects the closest server. The objective is to minimize the maximum time spent by any customer, including travel time and waiting time at the server sites. The problem is formulated and analyzed. Results for heuristic solution approaches are reported. Paper was partially supported by a College of Business Administration, California State University San Marcos summer grant of the first author. Paper was partially supported by an NSERC grant of the second author.     

Super efficiency in convex vector optimization

We establish a Lagrange Multiplier Theorem for super efficiency in convex vector optimization and express super efficient solutions as saddle points of appropriate Lagrangian functions. An example is given to show that the boundedness of the base of the ordering cone is essential for the existence of super efficient points.Research is supported partially by NSERC.Research is supported partially by NSERC and Mount St. Vincent University grant.     

On the failure of maximum entropy reconstruction for Fredholm equations and other infinite systems

We analyse several examples where the maximum entropy solution to a system of equations exists but fails to satisfy the natural (dual) formula. These examples highlight the role that finiteness of the number of constraints has in the efficacy of maximum entropy type estimation and reconstruction. We also provide two regularization processes which repair the problem.Research partially supported by NSERC grant OGP005116.     

Further arguments for slice convergence in nonreflexive spaces

It is shown that no notion of set convergence at least as strong as Wijsman convergence but not as strong as slice convergence can be preserved in superspaces. We also show that such intermediate notions of convergence do not always admit representations analogous to those given by Attouch and Beer for slice convergence, and provide a valid reformulation. Some connections between bornologies and the relationships between certain gap convergences for nonconvex sets are also observed.Research supported in part by an NSERC research grant and by the Shrum endowment.NSERC postdoctoral fellow.     

Cluster analysis and mathematical programming

Given a set of entities, Cluster Analysis aims at finding subsets, called clusters, which are homogeneous and/or well separated. As many types of clustering and criteria for homogeneity or separation are of interest, this is a vast field. A survey is given from a mathematical programming viewpoint. Steps of a clustering study, types of clustering and criteria are discussed. Then algorithms for hierarchical, partitioning, sequential, and additive clustering are studied. Emphasis is on solution methods, i.e., dynamic programming, graph theoretical algorithms, branch-and-bound, cutting planes, column generation and heuristics. Research supported by ONR grant N00014-95-1-0917, FCAR grant 95-ER-1048 and NSERC grants GP0105574 and GP0036426. The authors thank Olivier Gascuel and an anonymous referee for insightful remarks.