A multi-agent inventory problem with general transportation costs

This paper addresses the cost allocation problem that arises from an inventory system with multiple item and several agents that place joint orders according to an EOQ policy. In this setting, the cost per a new order has two components: a fixed cost and a variable cost. We assume that the variable part is given by a general function, not necessarily additive. We obtain the optimal policy and we evaluate some proposals of allocation rule for the ordering costs.     

Existence of infinitely many homoclinic orbits in discrete Hamiltonian systems

By using the Symmetric Mountain Pass Theorem, we establish some existence criteria to guarantee the second-order self-adjoint discrete Hamiltonian system Δ[p(n)Δu(n−1)]−L(n)u(n)+∇W(n,u(n))=0 has infinitely many homoclinic orbits, where n∈Z, u∈RN, p,L:Z→RN×N and W:Z×RN→R are no periodic in n. Our conditions on the potential W(n,x) are rather relaxed.     

Infinitely many homoclinic orbits for the second-order Hamiltonian systems

In this paper, the existence of homoclinic orbits for the second-order Hamiltonian systems without periodicity is studied and infinitely many homoclinic orbits for both superlinear and asymptotically linear cases are obtained.     

Constructions of strict Lyapunov functions for discrete time and hybrid time-varying systems

We provide explicit closed form expressions for strict Lyapunov functions for time-varying discrete time systems. Our Lyapunov functions are expressed in terms of known nonstrict Lyapunov functions for the dynamics and finite sums of persistency of excitation parameters. This provides a discrete time analog of our previous continuous time Lyapunov function constructions. We also construct explicit strict Lyapunov functions for systems satisfying nonstrict discrete time analogs of the conditions from Matrosov’s Theorem. We use our methods to build strict Lyapunov functions for time-varying hybrid systems that contain mixtures of continuous and discrete time evolutions.     

A discrete Newton algorithm for minimizing a function of many variables

A Newton-like method is presented for minimizing a function ofn variables. It uses only function and gradient values and is a variant of the discrete Newton algorithm. This variant requires fewer operations than the standard method whenn > 39, and storage is proportional ton rather thann ².     

Infinitely many homoclinic solutions for some second order Hamiltonian systems

In this paper, we investigate the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems. By using fountain theorem due to Zou, we obtain two new criteria for guaranteeing that second order Hamiltonian systems have infinitely many homoclinic solutions. Recent results in the literature are generalized and significantly improved.     

Riccati inequality and other results for discrete symplectic systems

In this paper we establish several new results regarding the positivity and nonnegativity of discrete quadratic functionals F associated with discrete symplectic systems. In particular, we derive (i) the Riccati inequality for the positivity of F with separated endpoints, (ii) a characterization of the nonnegativity of F for the case of general (jointly varying) endpoints, and (iii) several perturbation-type inequalities regarding the nonnegativity of F with zero endpoints. Some of these results are new even for the special case of discrete Hamiltonian systems.     

A new general decay for a transmission problem of viscoelastic Timoshenko systems

In this paper, we investigate the long-time behavior for a transmission problem of viscoelastic Timoshenko systems with different speeds of wave propagation. By constructing a new Lyapunov functional and combining the technique of perturbation energy with some precise estimates for multipliers, we establish a general uniform decay estimates for the energy.     

A faster polynomial algorithm for the unbalanced Hitchcock transportation problem

We present a new algorithm for the Hitchcock transportation problem. On instances with n sources and k sinks, our algorithm has a worst-case running time of O(nk²(logn+klogk)). It closes a gap between algorithms with running time linear in n but exponential in k and a polynomial-time algorithm with running time O(nk²log²n).     

Infinitely many solutions for a zero mass Schodinger-Poisson-Slater problem with critical growth

In this paper, we are concerned with the following Schr\"{o}dinger-Poisson-Slater problem with critical growth: $$ -\Delta u+(u^{2}\star \frac{1}{|4\pi x|})u=\mu k(x)|u|^{p-2}u+|u|^{4}u\,\,\mbox{in}\,\,\R^{3}. $$ We use a measure representation concentration-compactness principle of Lions to prove that the $(PS)_{c}$ condition holds locally. Via a truncation technique and Krasnoselskii genus theory, we further obtain infinitely many solutions for $\mu\in(0,\mu^{\ast})$ with some $\mu^{\ast}>0$.     

Equivalence between some definitions for the optimal mass transport problem and for the transport density on manifolds

In this paper we consider three problems, which are related to the classical Monges optimal mass transport problem and which are known to be equivalent when the ambient space is an open, convex and bounded subset of ⁿ; to these problems there correspond different definitions of particular measures (often called transport densities), which are also known to be equivalent. Here we will generalize the setting of these problems and the resulting definitions of transport densities to the case of a Riemannian manifold endowed with a finslerian semidistance, and we will see that the equivalences still hold. Mathematics Subject Classification (2000) 46G10, 49Q20, 58C35     

The linear quadratic minimum-time problem for a class of discrete systems

We consider a linear discrete-time systems controlled by inputs on L ²([0, t _N ], U), where (t _i )_{1?≤?i?≤?N} is a given sequence of times. The final time t _N (or N) is considered to be free. Given an initial state x ₀ and a final one x _d , we investigate the optimal control which steers the system from x ₀ to x _d with a minimal cost J(N, u) that includes the final time and energy terms. We treat this problem for both infinte and finite dimensional state space. We use a method similar to the Hilbert Uniqueness Method. A numerical simulation is given.     

On the global periodicity of discrete dynamical systems and application to rational difference equations

A new necessary condition for global periodicity of discrete dynamical systems and of difference equations is obtained here. This condition will be applied to contribute to solving the problem of global periodicity for second order rational difference equations.     

Nonlinear discrete systems with global boundary conditions

This paper is devoted to the study of boundary value problems on infinite time intervals for nonlinear, discrete-time systems. For problems of the form

     

A polynomial algorithm for an integer quadratic non-separable transportation problem

We study the problem of minimizing the total weighted tardiness when scheduling unti-length jobs on a single machine, in the presence of large sets of identical jobs. Previously known algorithms, which do not exploit the set structure, are at best pseudo-polynomial, and may be prohibitively inefficient when the set sizes are large. We give a polynomial algorithm for the problem, whose number of operations is independent of the set sizes. The problem is reformulated as an integer program with a quadratic, non-separable objective and transportation constraints. Employing methods of real analysis, we prove a tight proximity result between the integer solution to that problem and a fractional solution of a related problem. The related problem is shown to be polynomially solvable, and a rounding algorithm applied to its solution gives the optimal integer solution to the original problem.Supported in part by the National Science Foundation under grant ECS-85-01988, and by the Office of Naval Research under grant N00014-88-K-0377.Supported in part by Allon Fellowship, by Air Force grants 89-0512 and 90-0008 and by DIMACS (Center for Discrete Mathematics and Theoretical Computer Science), a National Science Foundation Science and Technology Center—NSF-STC88-09648. Part of the research of this author was performed in DIMACS Center, Rutgers University.Supported in part by Air Force grant 84-0205.     

带有运输且加工具有灵活性的无等待流水作业排序问题

研究一类带有运输且加工具有灵活性的两阶段无等待流水作业排序问题, 其中每阶段只有一台机器, 每个工件有两道工序需要依次在两台机器上加工, 工件在两台机器上的加工及两道工序之间不允许等待. 给出两种近似算法, 并分别分析其最坏情况界. 第一种算法是排列排序, 证明了最坏情况界不超过5/2; 第二种算法将工件按照两道工序加工时间之和的递增顺序排序, 证明其最坏情况界不超过2. 最后, 通过数值模拟比较算法的性能. 对问题中各参数取不同值的情况, 分别生成若干个实例, 用算法得到的解与最优解的下界作比值, 通过分析这些比值的最大值、最小值和平均值来比较上述两个算法的性能.