When the estimation of the single equation multiple linear regression model is looked upon as an optimization problem, we show how the principles and methods of optimization can assist the analyst in finding an attrac...
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When the estimation of the single equation multiple linear regression model is looked upon as an optimization problem, we show how the principles and methods of optimization can assist the analyst in finding an attractive prediction model. We illustrate this with the estimation of a linear prediction model for valuating residential property using regression quantiles. We make use of the linear parametric programming formulation to obtain the family of regression quantile models associated with a data set. We use the principle of dominance to reduce the number of models for consideration in the search for the most preferred property valuation model (s). We also provide useful displays that assist the analyst and the decision maker in selecting the final model (s). The approach is an interface between data analysis and operations research. (C) 2011 Elsevier B.V. All rights reserved.
In this paper, we propose the use of lexicographic parametric programming to recognize efficient units in data envelopment analysis (DEA). By using the parameterization of the right-hand side vector of the envelopment...
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In this paper, we propose the use of lexicographic parametric programming to recognize efficient units in data envelopment analysis (DEA). By using the parameterization of the right-hand side vector of the envelopment problem, we obtain the efficiency curve which is traversing through the efficient frontier from unit to unit. The units in the basis with any parameter value are efficient and the unit dominated by a point on an efficient facet is inefficient. Lexicographic parametric programming is needed to guarantee that all units to be considered are efficient-not only weakly efficient. (c) 2005 Elsevier Ltd. All rights reserved.
In this work, we present a new algorithm for solving complex multi-stage optimization problems involving hard constraints and uncertainties, based on dynamic and multi-parametric programming techniques. Each echelon o...
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In this work, we present a new algorithm for solving complex multi-stage optimization problems involving hard constraints and uncertainties, based on dynamic and multi-parametric programming techniques. Each echelon of the dynamic programming procedure, typically employed in the context of multi-stage optimization models, is interpreted as a multi-parametric optimization problem, with the present states and future decision variables being the parameters, while the present decisions the corresponding optimization variables. This reformulation significantly reduces the dimension of the original problem, essentially to a set of lower dimensional multi-parametric programs, which are sequentially solved. Furthermore, the use of sensitivity analysis circumvents non-convexities that naturally arise in constrained dynamic programming problems. The potential application of the proposed novel framework to robust constrained optimal control is highlighted.
In this work an improved B&B algorithm for MINLPs is proposed. The basic idea of the proposed algorithm is to treat binary variables as parameters and obtain the solution of the resulting multi-parametric NLP (mp-...
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In this work an improved B&B algorithm for MINLPs is proposed. The basic idea of the proposed algorithm is to treat binary variables as parameters and obtain the solution of the resulting multi-parametric NLP (mp-NLP) as a function of the binary variables, relaxed as continuous variables, at the root node of the search tree. It is recognized that solving the mp-NLP at the root node can be more computationally expensive than exhaustively enumerating all the terminal nodes of the tree. Therefore, only a local approximate parametric solution, and not a complete map of the parametric solution, is obtained and it is then used to guide the search in the tree. (c) 2012 Elsevier Ltd. All rights reserved.
We propose a solution to moving-horizon state estimation that incorporates inequality constraints in both a systematic and computationally efficient way, akin to Kalman filtering. The proposed method allows the on-lin...
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We propose a solution to moving-horizon state estimation that incorporates inequality constraints in both a systematic and computationally efficient way, akin to Kalman filtering. The proposed method allows the on-line constrained optimization problem involved in moving-horizon state estimation to be solved offline, requiring only a look-up table and simple function evaluations for real-time implementation. The method is illustrated via simulations on a system that has been studied in literature. (c) 2007 Elsevier Ltd. All rights reserved.
An advanced model-based control technique for regulating the blood glucose for patients with Type 1 diabetes is presented. The optimal insulin delivery rate is obtained off-line as an explicit function of the current ...
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An advanced model-based control technique for regulating the blood glucose for patients with Type 1 diabetes is presented. The optimal insulin delivery rate is obtained off-line as an explicit function of the current blood glucose concentration of the patient by using novel parametric programming algorithms, developed at Imperial College London. The implementation of the optimal insulin delivery rate, therefore, requires simple function evaluation and minimal on-line computations. The proposed framework also addresses the uncertainty in the model due to interpatient and intrapatient variability by identifying the model parameters which ensure that a feasible control law can be obtained. The developments reported in this paper are expected to simplify the insulin delivery mechanism, thereby enhancing the quality of life of the patient.
This paper proposes a modeling methodology for supply chain operations with a focus on the relationships of supply chain entities. Supply chain operation problems are mathematically formulated into a multilevel progra...
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This paper proposes a modeling methodology for supply chain operations with a focus on the relationships of supply chain entities. Supply chain operation problems are mathematically formulated into a multilevel programming problem. A multiparametric programming-based computation methodology is proposed to compute the solution of the problems. Numerical examples are presented to illustrate the proposed modeling and computational methodology with some remarks.
This paper brings together two fundamental topics: polyhedral projection and parametric linear programming. First, it is shown that, given a parametric linear program (PLP), a polyhedron exists whose projection provid...
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This paper brings together two fundamental topics: polyhedral projection and parametric linear programming. First, it is shown that, given a parametric linear program (PLP), a polyhedron exists whose projection provides the solution to the PLP. Second, the converse is tackled and it is shown how to formulate a PLP whose solution is the projection of an appropriately defined polyhedron described as the intersection of a finite number of halfspaces. The input to one operation can be converted to an input of the other operation and the resulting output can be converted back to the desired form in polynomial time-this implies that algorithms for computing projections or methods for solving parametric linear programs can be applied to either problem class.
作者：
BEREANU, BUNIV BONN
SONDER FORSCH BEREICH 72D-5300 BONN 1FED REP GER MINIST EDUC
CTR MATH STATISTICSBUCHARESTROMANIA
It is proved a sufficient condition that the optimal value of a linear program be a continuous function of the coefficients. The condition isessential, in the sense that, if it is not imposed, then examples with disco...
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It is proved a sufficient condition that the optimal value of a linear program be a continuous function of the coefficients. The condition isessential, in the sense that, if it is not imposed, then examples with discontinuous optimal-value function may be found. It is shown that certain classes of linear programs important in applications satisfy this condition. Using the relation between parametric linear programming and the distribution problem in stochastic programming, a necessary and sufficient condition is given that such a program has optimal value. Stable stochastic linear programs are introduced, and a sufficient condition of such stability, important in computation problems, is established.
The transportation problem is an important and relevant supply chain optimization problem in the traffic engineering. This paper minimizes shipping costs of a three channel distribution system comprised of plants, dis...
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The transportation problem is an important and relevant supply chain optimization problem in the traffic engineering. This paper minimizes shipping costs of a three channel distribution system comprised of plants, distribution centers, and customers. Plants manufacture several products that are delivered to distribution centers. If a distribution center is used then fixed cost is charged. Customers are replenished by an only one distribution center. To characterize the uncertainty that typically occurs in many practical decision environments, this paper considers the supply capacities, demands as Gaussian type-2 fuzzy variables. To provide a modelling framework for optimization problems with multi-fold uncertainty, different reduction methods are proposed to transform a Gaussian type-2 fuzzy variable into a type-1 fuzzy variable by mean reduction method. Then the transportation problem is reformulated as a chance-constrained expected value model enlightened by the credibility optimization method. The deterministic models are then solved using two different soft computing techniques (i) Generalized Reduced Gradient (Lingo-14.0), and (ii) modified Particle Swarm Optimization(PSO), where the position of each particle is adjusted according to its own experience and that of its neighbors. The numerical experiments illustrate the application and effectiveness of the proposed solution approaches.
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