The anisotropic mesh size function represented by metric tensors includes two features: mesh sizes and mesh orientation. Such metrics are widely used in scientific computing for adaptation, but the solution metrics ar...
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ISBN:
(数字)9781624105951
ISBN:
(纸本)9781624105951
The anisotropic mesh size function represented by metric tensors includes two features: mesh sizes and mesh orientation. Such metrics are widely used in scientific computing for adaptation, but the solution metrics are not smooth, which adversely affects adaptation. A novel algorithm is proposed in this paper to smooth the metric as a whole and to improve anisotropic mesh size gradation. First, the concept of Log-Euclidean metrics is used to convert the metric tensors from the Riemannian space into a Euclidean space. Then, the variations of metric tensors are limited by constraining the gradients of metric tensors in this space over the region of each background mesh element. Finally, a convex nonlinear optimization problem is formulated to smooth the metric tensors over the entire meshing domain. Theoretical analysis reveals the existence of a globally optimal smoothed sizing function. Numerical experiments on anisotropic meshes are presented to demonstrate the effectiveness of the proposed method.
This article is about placement of interconnected facilities (equipment) in a plane on parallel lines with forbidden zones. Placement of the facilities inside of the forbidden zones is not possible. The facilities are...
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This article is about placement of interconnected facilities (equipment) in a plane on parallel lines with forbidden zones. Placement of the facilities inside of the forbidden zones is not possible. The facilities are connected to each other and with the zones by some communications. Communications (routing of communications) between the facilities and between the facilities and zones which are placed on different lines (adjacent lines) pass through a fixed vertical component (viaduct). It is need to place the facilities on the lines such a way that the total cost of communications between the facilities and zones will be minimal. There are many practical applications of this problem in science and techniques, for example, when designing engineering devices. Some properties of the problem are formulated. A mathematical model of integer nonlinear programming of the problem is constructed. It is shown that algorithms for solving of a problem with rectangular metric without the viaduct can be used for solving of the problem under consideration.
Using the methods of least squares and optimization, a mathematical model is established based on the running model of Joseph B. Keller, and combining the running characteristics and actual conditions of athletes. Who...
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ISBN:
(纸本)9781728176840
Using the methods of least squares and optimization, a mathematical model is established based on the running model of Joseph B. Keller, and combining the running characteristics and actual conditions of athletes. Whole marathon is divided into three phases: the starting section, the halfway section and the sprint section. Different from previous studies, this study designs athletes to accelerate in the starting and the last stage of the race. But in the middle segment, it is an uniform motion. The study finds that the model design is in line with the objective facts of the marathon. Through this model, the relative errors between theoretical results and actual competition results can be found out realistically, so as to provide scientific training basis for marathon coaches and athletes to improve their running results. At the same time, this search proves that high-level athletes use uniform speed running in the middle of the competition, which is more conducive to exerting their level and showing better performance.
The purpose of this paper is to present a fuel-optimal low-thrust transfer problem and a convex approach that can be utilized to identify an optimal solution in real time. In our previous work, two slack variables wer...
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ISBN:
(数字)9781624105951
ISBN:
(纸本)9781624105951
The purpose of this paper is to present a fuel-optimal low-thrust transfer problem and a convex approach that can be utilized to identify an optimal solution in real time. In our previous work, two slack variables were introduced to aid in reducing the coupling of the control and state variables. This proves useful in transforming the problem into a convex optimization problem. The main contribution of this paper is that the original optimal control problem can be solved without the use of one of the previously defined slack variables. After eliminating one of these slack variables, the methodology developed in our previous work is followed. In this process the control and state variables are partially decoupled, the control constraints are convexified, and the original problem is translated into a sequence of convex optimization problems. The solution can then be found utilizing interior-point methods. The success and accuracy of this newly developed method is shown through numerical simulations of a minimum-fuel Earth-to-Mars low-thrust transfer problem. The results are compared to the effectiveness of the previous form of this solution process and analyzed for relative performance and efficiency.
In this paper, we propose a robust model predictive control algorithm for discrete-time nonholonomic robot systems with additive disturbances. To achieve moving obstacle avoidance, the related polyhedral over-approxim...
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ISBN:
(纸本)9781728190938
In this paper, we propose a robust model predictive control algorithm for discrete-time nonholonomic robot systems with additive disturbances. To achieve moving obstacle avoidance, the related polyhedral over-approximations are utilized to realize the reformulation of obstacle avoidance constraint. Thus, the resulting model predictive control optimization problem can be solved effectively by standard nonlinear programming solvers. Moreover, the theoretical guarantees for recursive feasibility and input-to-state stability are provided. Finally, the efficiency of the proposed algorithm is verified by the simulation results.
Increasingly complex hybrid electric vehicle (HEV) powertrains are being developed to address the growing stringency of emissions regulations, fuel economy standards and drivability/performance requirements. Early in ...
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We propose a derivative-free cubic regularization method for solving nonlinear systems of equations without available derivatives. The novel feature of the method is that, based on locally interpolation models, the se...
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We propose a derivative-free cubic regularization method for solving nonlinear systems of equations without available derivatives. The novel feature of the method is that, based on locally interpolation models, the search direction in each iteration is allowed to be a solution of a model-based cubic regularization approximation formulated by the special structure of equations that ensures a significant improvement. We present a set of wild conditions that the search direction must be satisfied so that the global convergence of the method for solving the nonlinear equations is guaranteed. The global convergence and the fast local convergence rate of the proposed method are established, and numerical experiments are provided to illustrate the reliability of the proposed method.
With the rise of online retailer giants like Amazon, and enhancements in internet and mobile technologies, online shopping is becoming increasingly popular. This has lead to new opportunities in online price optimizat...
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With the rise of online retailer giants like Amazon, and enhancements in internet and mobile technologies, online shopping is becoming increasingly popular. This has lead to new opportunities in online price optimization. The overarching motivation and theme of this thesis is to review these opportunities and provide methods and models in the context of retailers' online pricing decisions. In Chapter 2 a multi-period revenue maximization and pricing optimization problem in the presence of reference prices is formulated as a mixed integer nonlinear program. Two algorithms are developed to solve the optimization problem: a generalized Benders' decomposition algorithm and a myopic heuristic. This is followed by numerical computations to illustrate the effciency of the solution approaches as well as some managerial pricing insights. In Chapter 3 a data-driven quadratic programming optimization model for online pricing in the presence of customer ratings is proposed. A new demand function is developed for a multi-product, nite horizon, online retail environment. To solve the optimization problem, a myopic pricing heuristic as well as exact solution approaches are introduced. Using customer reviews ratings data from ***, a new customer rating forecasting model is validated. This is followed by several analytical and numerical insights. In Chapter 4 a multinomial choice model is used for customer purchase decision to find optimal personalized price discounts for an online retailer that incorporates customer locations and feedback from their reviews. Closed form solutions are derived for two special cases of this problem. To gain some analytical insights extensive numerical experiments are carried followed by several analytical and numerical insights. Thesis Doctor of Philosophy (PhD) The increase in online retail and the improvements in mobile technologies has lead to advantages and opportunities for both customers and retailers. One of these advantages is the abi
In order to solve correctly the task of searching for heliosynchronous orbits when the equations of motion become coupled due to the inclusion of sectoral terms in the disturbing potential, the concept of quasi-helios...
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This paper deals with modeling and fitting for epedimic models and their applications to the field of plants disease. For this purpose, two models are proposed that are expressed as a blend of two functions which refl...
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