Lagrangian Duality in Set-Valued Optimization

In this paper, we study optimization problems where the objective function and the binding constraints are set-valued maps and the solutions are defined by means of set-relations among all the images sets (Kuroiwa, D. in Takahashi, W., Tanaka, T. (eds.) Nonlinear analysis and convex analysis, pp. 221–228, 1999). We introduce a new dual problem, establish some duality theorems and obtain a Lagrangian multiplier rule of nonlinear type under convexity assumptions. A necessary condition and a sufficient condition for the existence of saddle points are given. The authors thank the two referees for valuable comments and suggestions on early versions of the paper. The research of the first author was partially supported by Ministerio de Educación y Ciencia (Spain) Project MTM2006-02629 and by Junta de Castilla y León (Spain) Project VA027B06.     

Solving large-scale semidefinite programs in parallel

We describe an approach to the parallel and distributed solution of large-scale, block structured semidefinite programs using the spectral bundle method. Various elements of this approach (such as data distribution, an implicitly restarted Lanczos method tailored to handle block diagonal structure, a mixed polyhedral-semidefinite subdifferential model, and other aspects related to parallelism) are combined in an implementation called LAMBDA, which delivers faster solution times than previously possible, and acceptable parallel scalability on sufficiently large problems. This work was supported in part by NSF grants DMS-0215373 and DMS-0238008.     

Improved modeling and solution methods for the multi-resource routing problem

This paper presents modeling and solution method improvements for the Multi-Resource Routing Problem (MRRP) with flexible tasks. The MRRP with flexible tasks is used to model routing and scheduling problems for intermodal drayage operations in which two resources (tractors and trailers) perform tasks to transport loaded and empty equipment. Tasks may be either well defined, in which both the origin and the destination of a movement are given, or flexible, in which the origin or the destination is chosen by the model. This paper proposes methods to effectively manage the number of options considered for flexible tasks (either feasible origins for a known destination or feasible destinations for a known origin). This modeling change generates sufficient options to allow for low-cost solutions while maintaining reasonable computational effort. We also propose a new solution method that uses randomized route generation. Computational results from test cases show that these changes improve the quality of solutions by at least 5% in the test cases as compared to methods from previous studies.     

Applications of inversion formulas to the joint t-universality of Lerch zeta functions

In this paper, we define λ-joint, a^′-joint, (λ,λ)-joint, (λ,a^′)-joint and (a^′,a^′)-joint t-universality of Lerch zeta functions and consider the relations among those. Next we show the existence of (λ,λ)-joint t-universality. Finally, we also show the existence of λ-joint, a^′-joint, (λ,a^′)-joint and (a^′,a^′)-joint t-universality by using inversion formulas.     

Semideterministic Global Optimization Method: Application to a Control Problem of the Burgers Equation

This paper has two objectives. We introduce a new global optimization algorithm reformulating optimization problems in terms of boundary-value problems. Then, we apply this algorithm to a pointwise control problem of the viscous Burgers equation, where the control weight coefficient is progressively decreased. The results are compared with those obtained with a genetic algorithm and an LM-BFGS algorithm in order to check the efficiency of our method and the necessity of using global optimization techniques.     

目标函数扰动的集值优化问题的稳定性

本文研究了由目标函数扰动的集值优化问题的有效点集所定义的集值映射的半连续性.讨论了目标函数扰动的集值优化问题在上半连续意义下的稳定性.特别地,在广义适定性条件下,证明了集值优化问题在上半连续意义下的稳定性.     

An optimization algorithm for a penalized knapsack problem

We study a variation of the knapsack problem in which each item has a profit, a weight and a penalty; the sum of profits of the selected items minus the largest penalty associated with the selected items must be maximized. We present an ILP formulation and an exact optimization algorithm.     

Portfolio optimization in stochastic markets

We consider a multiperiod mean-variance model where the model parameters change according to a stochastic market. The mean vector and covariance matrix of the random returns of risky assets all depend on the state of the market during any period where the market process is assumed to follow a Markov chain. Dynamic programming is used to solve an auxiliary problem which, in turn, gives the efficient frontier of the mean-variance formulation. An explicit expression is obtained for the efficient frontier and an illustrative example is given to demonstrate the application of the procedure.     

Dynamic Nonlinear Modelization of Operational Supply Chain Systems

Supply Chain Management (SCM) is an important activity in all producing facilities and in many organizations to enable vendors, manufacturers and suppliers to interact gainfully and plan optimally their flow of goods and services. To realize this, a dynamic modelling approach for characterizing supply chain activities is opportune, so as to plan efficiently the set of activities over a distributed network in a formal and scientific way. The dynamical system will result so complex that it is not generally possible to specify the functional forms and the parameters of interest, relating outputs to inputs, states and stochastic terms by experiential specification methods. Thus the algorithm that will presented is Data Driven, determining simultaneously the functional forms, the parameters and the optimal control policy from the data available for the supply chain. The aim of this paper is to present this methodology, by considering dynamical aspects of the system, the presence of nonlinear relationships and unbiased estimation procedures to quantify these relations, leading to a nonlinear and stochastic dynamical system representation of the SCM problem. Moreover, the convergence of the algorithm will be proved and the satisfaction of the required statistical conditions demonstrated. Thus SCM problems may be formulated as formal scientific procedures, with well defined algorithms and a precise calculation sequence to determine the best alternative to enact. A “Certainty equivalent principle” will be indicated to ensure that the effects of the inevitable uncertainties will not lead to indeterminate results, allowing the formulation of demonstrably asymptotically optimal management plans.     

一个新的最优模糊存储模型

提出一个新的具有积压定单的关于模糊订购量的模糊存储模型.在模糊函数原理下,给出了模糊总存储成本.为了寻找最优解,把最优模糊存储模型转化为双目标最优化模型,利用L ingo8.0求解不等式约束问题,我们发现最优解都是确定的实数.此外,当模糊订购量和模糊总需求都是三角形(或权重均为1/2梯形)模糊数时,我们提出模型的最优解与经典的具有积压定单存储模型具有相同的结果.