An Algorithm for Solving Scaled Total Least Squares Problems
... total least squares problems using the rank revealing ULV decomposition, which is an approximation of the complete orthogonal decomposition. To improve accuracy, in addition to the refinement, we proposed a technique for improving the accuracy of the estimates for the smallest nonzero singular value ...
... total least squares problems using the rank revealing ULV decomposition, which is an approximation of the complete orthogonal decomposition. To improve accuracy, in addition to the refinement, we proposed a technique for improving the accuracy of the estimates for the smallest nonzero singular value ...
Optimal Conditioning of Quasi-Newton Methods
... IV. Computational Results. The five methods for selecting t discussed in Section III were tested on the four test problems documented in [6]. As previous testing included the straight Fletcher-Powell and Barnes-Rosen [1], [5] techniques, they are not included here. Previous tests have shown both to ...
... IV. Computational Results. The five methods for selecting t discussed in Section III were tested on the four test problems documented in [6]. As previous testing included the straight Fletcher-Powell and Barnes-Rosen [1], [5] techniques, they are not included here. Previous tests have shown both to ...
Activity Notes
... that the best location would be one that minimizes the average distance to one of the houses. Let’s call this B1. Ask for other ideas. If someone does not suggest it, suggest that an alternative definition would be to minimize the maximum distance the fire truck would need to travel. Let’s call this ...
... that the best location would be one that minimizes the average distance to one of the houses. Let’s call this B1. Ask for other ideas. If someone does not suggest it, suggest that an alternative definition would be to minimize the maximum distance the fire truck would need to travel. Let’s call this ...
An Eulerian-Lagrangian method for optimization problems governed
... If = R2 , then (1.1b) is supplemented by appropriate boundary conditions. In recent years, there has been tremendous progress in both analytical and numerical studies of problems of type (1.1a), (1.1b), see, e.g., [1–3,8–10,13,18,19,21– 24,28,40,44,45]. Its solution relies on the property of the ...
... If = R2 , then (1.1b) is supplemented by appropriate boundary conditions. In recent years, there has been tremendous progress in both analytical and numerical studies of problems of type (1.1a), (1.1b), see, e.g., [1–3,8–10,13,18,19,21– 24,28,40,44,45]. Its solution relies on the property of the ...
Test your understanding of matching and equational reasoning.
... will have the form t s and will have a solution if there exists a substitution σ such that σ(t) = s where = denotes a boolean test for syntactic equality. IMPORTANT NOTE: The substitution σ should only be applied to one side of the match equation. That is, in the match equation t s, sigma should ...
... will have the form t s and will have a solution if there exists a substitution σ such that σ(t) = s where = denotes a boolean test for syntactic equality. IMPORTANT NOTE: The substitution σ should only be applied to one side of the match equation. That is, in the match equation t s, sigma should ...
Uniqueness of solutions to the Laplace and Poisson equations
... 6. Why is the Poisson equation with Cauchy boundary conditions ill-posed? In the case of Cauchy boundary conditions (where both u and ∂u/∂n are simultaneously specified on S), the same arguments employed above can again be used to prove that if a solution exists it must be unique. Unfortunately, in ...
... 6. Why is the Poisson equation with Cauchy boundary conditions ill-posed? In the case of Cauchy boundary conditions (where both u and ∂u/∂n are simultaneously specified on S), the same arguments employed above can again be used to prove that if a solution exists it must be unique. Unfortunately, in ...
A Heuristic for a Mixed Integer Program using the Characteristic
... using the LP-based branch and bound (BB) solvers or with stochastic search-based solvers (Noraini and Geraghty, 2011). In reality MIP solvers have implemented more sophisticated versions denoted by branch and cut (BC) algorithms (Sen and Sherali, 2006). With the increase in the application of both P ...
... using the LP-based branch and bound (BB) solvers or with stochastic search-based solvers (Noraini and Geraghty, 2011). In reality MIP solvers have implemented more sophisticated versions denoted by branch and cut (BC) algorithms (Sen and Sherali, 2006). With the increase in the application of both P ...
Multiple-criteria decision analysis
Multiple-criteria decision-making or multiple-criteria decision analysis (MCDA) is a sub-discipline of operations research that explicitly considers multiple criteria in decision-making environments. Whether in our daily lives or in professional settings, there are typically multiple conflicting criteria that need to be evaluated in making decisions. Cost or price is usually one of the main criteria. Some measure of quality is typically another criterion that is in conflict with the cost. In purchasing a car, cost, comfort, safety, and fuel economy may be some of the main criteria we consider. It is unusual that the cheapest car is the most comfortable and the safest one. In portfolio management, we are interested in getting high returns but at the same time reducing our risks. Again, the stocks that have the potential of bringing high returns typically also carry high risks of losing money. In a service industry, customer satisfaction and the cost of providing service are two conflicting criteria that would be useful to consider.In our daily lives, we usually weigh multiple criteria implicitly and we may be comfortable with the consequences of such decisions that are made based on only intuition. On the other hand, when stakes are high, it is important to properly structure the problem and explicitly evaluate multiple criteria. In making the decision of whether to build a nuclear power plant or not, and where to build it, there are not only very complex issues involving multiple criteria, but there are also multiple parties who are deeply affected from the consequences.Structuring complex problems well and considering multiple criteria explicitly leads to more informed and better decisions. There have been important advances in this field since the start of the modern multiple-criteria decision-making discipline in the early 1960s. A variety of approaches and methods, many implemented by specialized decision-making software, have been developed for their application in an array of disciplines, ranging from politics and business to the environment and energy.