With the help of a logarithmic barrier augmented Lagrangian function, we can obtain closed-form solutions of slack variables of logarithmic-barrier problems of nonlinear programs. As a result, a two-parameter primal-d...
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With the help of a logarithmic barrier augmented Lagrangian function, we can obtain closed-form solutions of slack variables of logarithmic-barrier problems of nonlinear programs. As a result, a two-parameter primal-dual nonlinear system is proposed, which corresponds to the Karush-Kuhn-Tucker point and the infeasible stationary point of nonlinear programs, respectively, as one of two parameters vanishes. Based on this distinctive system, we present a primal-dual interior-point method capable of rapidly detecting infeasibility of nonlinear programs. The method generates interior-point iterates without truncation of the step. It is proved that our method converges to a Karush-Kuhn-Tucker point of the original problem as the barrier parameter tends to zero. Otherwise, the scaling parameter tends to zero, and the method converges to either an infeasible stationary point or a singular stationary point of the original problem. Moreover, our method has the capability to rapidly detect the infeasibility of the problem. Under suitable conditions, the method can be superlinearly or quadratically convergent to the Karush-Kuhn-Tucker point if the original problem is feasible, and it can be superlinearly or quadratically convergent to the infeasible stationary point when the problem is infeasible. Preliminary numerical results show that the method is efficient in solving some simple but hard problems, where the superlinear convergence to an infeasible stationary point is demonstrated when we solve two infeasible problems in the literature.
The reactive power optimization and reconfiguration of traditional distribution network are mostly studied separately, lacking the coordination and cooperation of different optimization techniques. A mathematical mode...
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In this paper,we establish a logit model to evaluate the non-default probability of small and medium-sized *** on the data from 2020 National Mathematics Competition for College Students,we construct financial indicat...
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In this paper,we establish a logit model to evaluate the non-default probability of small and medium-sized *** on the data from 2020 National Mathematics Competition for College Students,we construct financial indicators and credibility indicators,using BP neural network and logistic regression to calculate the probability of small and medium-sized enterprises’not ***,we use nonlinear programming to optimize banks’credit decision and give the specific loan amounts of each small and medium-sized enterprise.
This study focuses on developing continuous reactor network models able to produce multiple rigid polyol products under strict product and safety specifications. We first determine reactor networks and operating decis...
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State-of-the-art engine models are used to study the emissions production, and fuel consumption minimization, of a typical diesel-powered road car operating on a variable-gradient road. The engine models, which have b...
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State-of-the-art engine models are used to study the emissions production, and fuel consumption minimization, of a typical diesel-powered road car operating on a variable-gradient road. The engine models, which have been fit to measured test cell data, are used to represent both the performance and emissions generation characteristics of a typical diesel-fuelled car engine. A simple example is used to highlight the impact of elevation changes on the main structural features of fuel optimal control problems (OCPs). A typical semiurban test route with legislated speed limits and enforced stops is used for performance evaluation purposes. The optimal functioning of a discrete-gear automatic transmission system, as opposed to a simple continuously variable transmission, is studied in detail. The main focus of this paper is to evaluate the importance of 3-D road influences (gradient and curvature), preimposed time-of-arrival constraints, enforced stops, and emissions constraints on the fuel consumption and optimal driving of typical diesel-powered road vehicles. This paper proposes the use of multiple-phase optimal control to elicit a better understanding of "real" driving situations and motivates a move away from standardized drive cycles.
This work proposes a cluster oriented channel assignment and difference of two convex functions (d.c.) programming based power optimisation algorithm for the downlink device-to-device (D2D) communication underlaying c...
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This work proposes a cluster oriented channel assignment and difference of two convex functions (d.c.) programming based power optimisation algorithm for the downlink device-to-device (D2D) communication underlaying cellular networks. The authors' objective is to maximise D2D throughput while protecting the performance of existing cellular users (CUs) whose channel is reused among multiple D2D pairs, by imposing a minimum rate requirement constraint on each CU. The joint channel and power optimisation problem is a mixed integer non-linear programming problem that is NP-hard to solve. Therefore, a three stage solution is proposed: cluster formation to minimise the interference among the D2D pairs followed by an optimal channel assignment using the Hungarian algorithm and then an iterative power optimisation algorithm based on d.c. programming. Moreover, the transmission power of base station and D2D users is optimised on the same channel while considering the mutual interference among D2D pairs. Numerical results verify the effectiveness of the proposed resource allocation scheme in terms of the D2D sum rate and the number of successful transmission of D2D users. Moreover, the iterative power optimisation algorithm shows a fast convergence behaviour. In addition to this, the energy efficiency is also analysed with respect to various parameters.
A permanent magnet (PM) with an accurate magnetization distribution is required for the design of high-quality electrical machines. The nondestructive diagnosis of the magnetization distribution in PM is essential to ...
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A permanent magnet (PM) with an accurate magnetization distribution is required for the design of high-quality electrical machines. The nondestructive diagnosis of the magnetization distribution in PM is essential to facilitate the practical design of the synchronous machines. While some methods for magnetization evaluation have been proposed, an optimal method has not been established due to the indefiniteness of the magnetization distribution. Then, the method using nonlinear programming based on the 1-D Fourier series expansion has been proposed by the authors. In this article, the method based on the 2-D Fourier expansion is proposed. The performance of the proposed method was demonstrated in PM, in which orientations were set to parallel and polar isotropic. The performance of the proposed method is compared with the singular value decomposition method.
We present a novel variational inequality model (VIM) to capture the complex real decision-making process in multi-tiered supply chain networks (MSCN) without strictly limiting the features of related functions. The V...
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Delay differential equations have a wide range of applications in science and engineering. When these equations are nonlinear, we cannot usually obtain an exact solution. Hence, we must utilize an efficient numerical ...
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Delay differential equations have a wide range of applications in science and engineering. When these equations are nonlinear, we cannot usually obtain an exact solution. Hence, we must utilize an efficient numerical method with high convergence rate and low error to approximate the solution. In this paper, we propose a new shifted pseudospectral method to solve nonlinear delay differential equations. First, we convert the problem into an equivalent continuous-time optimization problem and then use a pseudospectral method to discretize the problem. By solving the obtained discrete-time problem, we achieve an approximate solution for the main delay differential equation. Here, we analyze the convergence of the method and solve some practical delay differential equations to show the efficiency of the method.
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