To meet the requirement of constrained delay and computation resource of the future vehicular networks, it is imperative to develop efficient content caching strategy and computation resource allocation strategy in mo...
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To meet the requirement of constrained delay and computation resource of the future vehicular networks, it is imperative to develop efficient content caching strategy and computation resource allocation strategy in mobile edge computing (MEC) servers. In the proposed network framework, since the caching capacity and computing resource of each MEC are limited, and the coverage areas of MECs are overlapped, the vehicular networks have to decide what contents to cache, how to offload tasks and how much computing resource needs to be allocated for each task. In this study, in order to jointly tackle these issues, we formulate caching strategy, offloading decision and computing resource allocation coordinately as a mixed integer non-linear programming (MINLP) problem. To solve the MINLP problem, we divide it into two subproblems. Firstly, we investigate a balanced and efficient caching strategy based on similarity in vehicular networks. Secondly, we apply McCormick Envelopes to convert MINLP problem into LP problem, and then adopt improved branch and bound algorithm to obtain the optimal offloading decision and computing resource allocation strategy. Simulation results indicate that the proposed schemes have a good performance in reducing economic cost under the deadline of each task.
In this paper, a new class of unified penalty functions are derived for the semi-infinite optimization problems, which include many penalty functions as special cases. They are proved to be exact in the sense that und...
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In this paper, a new class of unified penalty functions are derived for the semi-infinite optimization problems, which include many penalty functions as special cases. They are proved to be exact in the sense that under Mangasarian-Fromovitz constraint qualification conditions, a local solution of penalty problem is a corresponding local solution of original problem when the penalty parameter is sufficiently large. Furthermore, global convergence properties are shown under some conditions. The paper is concluded with some numerical examples proving the applicability of our methods to PID controller design and linear-phase FIR digital filter design.
We present a primal-dual modified log-barrier algorithm to solve inequality constrained nonlinear optimization problems. Basically, the algorithm is a Newton-like method applied to a perturbation of the optimality sys...
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We present a primal-dual modified log-barrier algorithm to solve inequality constrained nonlinear optimization problems. Basically, the algorithm is a Newton-like method applied to a perturbation of the optimality system that follows from a reformulation of the initial problem by introducing a modified log-barrier function to handle inequality constraints. The algorithm uses an outer/inner iteration scheme and the globalization is performed in the primal-dual space by means of a new primal-dual merit function. The robustness and efficiency of the algorithm is improved using quadratic extrapolation. The numerical performance of the new method is illustrated by comparing it with a primal-dual classical log-barrier method and two well-established interior-point solvers on two sets of problems from COPS and Hock-Schittkowski collections, including a set of problems that exhibits degeneracy.
Deformable boring bar is the executive component of embedded giant magnetostrictive actuator (GMA), which plays a key role in the output performance of embedded GMA in precision machining of non-cylindrical piston pin...
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Deformable boring bar is the executive component of embedded giant magnetostrictive actuator (GMA), which plays a key role in the output performance of embedded GMA in precision machining of non-cylindrical piston pinhole. In this paper, a multi-parametric coupling design method was presented for deformable boring bar and giant magnetostrictive material. Firstly, the dynamic model of deformable boring bar was built. Second, the performance index of length-diameter ratio was introduced, and the problem of multi-parametric coupling design was solved by using the idea of nonlinear programming. The first-order natural frequency, the end output displacement and the output force of deformable boring bar were taken as the evaluation indexes to ensure the performance requirements of embedded GMA. Finally, according to project requirements and proposed method, an embedded GMA with high frequency response and large output displacement was further designed, which met the performance requirements of displacement and stiffness in precision machining of non-cylindrical piston pinholes and also verified the validity of the design method.
Group purchasing organizations (GPOs) aim to aggregate the purchasing requirements of many buyers and utilize economies of scale to save costs and obtain quantity discounts from suppliers. This paper extends the appli...
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Group purchasing organizations (GPOs) aim to aggregate the purchasing requirements of many buyers and utilize economies of scale to save costs and obtain quantity discounts from suppliers. This paper extends the application of GPOs to the chain stores industry. A new retailer is going to enter the market and faces decisions on joining chain stores (as a GPO) or independently working with a supplier, product pricing, and serving different segments of the market (i.e., informed and uninformed customers). When joining the GPO, a membership fee must be paid to the GPO. The supplier offers a quantity discount schedule that depends on the contract administration fee paid to the GPO. Using nonlinear programming, the optimal decision-making policy is established in a closed-form format. The results show that all decisions are significantly affected by the proportion of informed customers in the market. Accordingly, when the proportion of the informed customers is less than a threshold, not joining the GPO is a great choice for the retailer. When this proportion is growing, the retailer is advised to join the GPO as soon as possible. Our findings indicate that, in the presence of rapid growth of information technologies which leads to an increase in people's awareness of the market, GPOs play a strategic role in the chain stores industry nowadays. We demonstrate that GPOs not only provide many benefits for customers and retailers but also other players in the group purchasing chain would also profit.
The objective of this paper is to present an approximation-based strategy for solving the problem of nonlinear trajectory optimization with the consideration of probabilistic constraints. The proposed method defines a...
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The objective of this paper is to present an approximation-based strategy for solving the problem of nonlinear trajectory optimization with the consideration of probabilistic constraints. The proposed method defines a smooth and differentiable function to replace probabilistic constraints by the deterministic ones, thereby converting the chance-constrained trajectory optimization model into a parametric nonlinear programming model. In addition, it is proved that the approximation function and the corresponding approximation set will converge to that of the original problem. Furthermore, the optimal solution of the approximated model is ensured to converge to the optimal solution of the original problem. Numerical results, obtained from a new chance-constrained space vehicle trajectory optimization model and a 3-D unmanned vehicle trajectory smoothing problem, verify the feasibility and effectiveness of the proposed approach. Comparative studies were also carried out to show the proposed design can yield good performance and outperform other typical chance-constrained optimization techniques investigated in this paper.
Random projections map a set of points in a high dimensional space to a lower dimensional one while approximately preserving all pairwise Euclidean distances. Although random projections are usually applied to numeric...
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Random projections map a set of points in a high dimensional space to a lower dimensional one while approximately preserving all pairwise Euclidean distances. Although random projections are usually applied to numerical data, we show in this paper that they can be successfully applied to quadratic programming formulations over a set of linear inequality constraints. Instead of solving the higher-dimensional original problem, we solve the projected problem more efficiently. This yields a feasible solution of the original problem. We prove lower and upper bounds of this feasible solution w.r.t. the optimal objective function value of the original problem. We then discuss some computational results on randomly generated instances, as well as a variant of Markowitz' portfolio problem. It turns out that our method can find good feasible solutions of very large instances.
In this paper, the stochastic user equilibrium model and its optimization conditions are studied. At the same time, the first and second order differential information of the objective function is reasonably used to d...
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nonlinear model predictive control (NMPC) can directly handle multi-input multi-output nonlinear systems and explicitly consider input and state constraints. However, the computational load for nonlinear programming (...
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nonlinear model predictive control (NMPC) can directly handle multi-input multi-output nonlinear systems and explicitly consider input and state constraints. However, the computational load for nonlinear programming (NLP) of large-scale systems limits the range of possible applications and degrades NMPC performance. An NLP sensitivity based approach, advanced-step NMPC, has been developed to address the online computational load. In addition, for cases where the NLP solving time exceeds one sampling time, two types of advanced-multi-step NMPC (amsNMPC), parallel and serial, have been proposed. However, in previous studies, a serial amsNMPC could not be applied to large-scale problems because of the size of extended Karush-Kuhn-Tucker matrix and its Schur complement decomposition, and the robustness was analyzed under a conservative assumption for memory effects. In this paper, we propose a serial amsNMPC using an extended sensitivity method to increase the online computation speed further. We successfully apply it to a large-scale air separation unit using the sparse matrix handling packages of Python, Pyomo, and k_aug tools. Furthermore, an auxiliary NLP formulation is defined to analyze the robustness. Using this with the key properties of an extended sensitivity matrix, we can prove robustness while avoiding the memory effects term. (C) 2020 Elsevier Ltd. All rights reserved.
Up to now, several numerical methods have been presented to solve finite horizon fractional optimal control problems by researchers, while solving fractional optimal control problems on infinite domain is a challengin...
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Up to now, several numerical methods have been presented to solve finite horizon fractional optimal control problems by researchers, while solving fractional optimal control problems on infinite domain is a challenging work. Hence, in this article, a numerical method is proposed to solve fractional infinite horizon optimal control problems. At the first stage, a domain transformation technique is used to map the infinite domain to a finite horizon. Also, fractional derivative defined on an unbounded domain is converted into an equivalent derivative on a finite domain. Then, a new shifted Legendre pseudospectral method is utilized to solve the obtained finite problem and a nonlinear programming problem is suggested to approximate the optimal solutions. Finally, some numerical examples are given to show the efficiency of the method.
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