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Unconstrained convex minimization based implicit Lagrangian twin extreme learning machine for classification (ULTELMC)

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APPLIED INTELLIGENCE 2020年第4期50卷 1327-1344页

作者： Borah, Parashjyoti Gupta, Deepak Natl Inst Technol Dept Comp Sci & Engn Yupia Arunachal Prade India

The recently proposed twin extreme learning machine (TELM) requires solving two quadratic programming problems (QPPs) in order to find two non-parallel hypersurfaces in the feature that brings in the additional requirement of external optimization toolbox such as MOSEK. In this paper, we propose implicit Lagrangian TELM for classification via unconstrained convex minimization problem (ULTELMC) and further suggest iterative convergent schemes which eliminates the requirement of external optimization toolbox generally required in solving the quadratic programming problems (QPPs) of TELM. The solutions to the dual variables of the proposed ULTELMC are obtained using iterative schemes containing 'plus' function which is not differentiable. To overcome this shortcoming, the generalized derivative approach and smooth approximation approaches are suggested. Further, to test the performance of the proposed approaches, classification performances are compared with support vector machine (SVM), twin support vector machine (TWSVM), extreme learning machine (ELM), twin extreme learning machine (TELM) and Lagrangian extreme learning machine (LELM). Moreover, non-requirement to solve QPPs makes the iterative schemes find the solution faster as compared to the reported methods that finds the solution in dual space. Computational times required in finding the solutions are also presented for comparison.

关键词： Extreme learning machine Unconstrained minimization Smoothing approaches quadratic programming problem Iterative schemes

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Model predictive control for deeply pipelined field-programmable gate array implementation: algorithms and circuitry

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IET CONTROL THEORY AND APPLICATIONS 2012年第8期6卷 1029-1041页

作者： Jerez, J. L. Ling, K. -V. Constantinides, G. A. Kerrigan, E. C. Univ London Imperial Coll Sci Technol & Med Dept Elect & Elect Engn London SW7 2AZ England Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Univ London Imperial Coll Sci Technol & Med Dept Aeronaut London SW7 2AZ England

Model predictive control (MPC) is an optimisation-based scheme that imposes a real-time constraint on computing the solution of a quadratic programming (QP) problem. The implementation of MPC in fast embedded systems presents new technological challenges. In this paper we present a parameterised field-programmable gate array implementation of a customised QP solver for optimal control of linear processes with constraints, which can achieve substantial acceleration over a general purpose microprocessor, especially as the size of the optimisation problem grows. The focus is on exploiting the structure and accelerating the computational bottleneck in a primal-dual interior-point method. We then introduce a new MPC formulation that can take advantage of the novel computational opportunities, in the form of parallel computational channels, offered by the proposed pipelined architecture to improve performance even further. This highlights the importance of the interaction between the control theory and digital system design communities for the success of MPC in fast embedded systems.

关键词： quadratic programming problem optimisation-based scheme predictive control Logic and switching circuits pipeline processing digital system design Multiprocessing systems deeply pipelined field-programmable gate array implementation pipelined architecture linear processes field programmable gate arrays parallel computational channels general purpose microprocessor model predictive control Parallel architecture quadratic programming primal-dual interior-point method Optimal control fast embedded systems customised QP solver real-time constraint optimal control

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Robust transmit pulse design

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IEE PROCEEDINGS-VISION IMAGE AND SIGNAL PROCESSING 2004年第3期151卷 170-174页

作者： Vo, B Cantoni, A Univ Melbourne Elect & Elect Engn Dept Parkville Vic 3010 Australia Western Australian Telecommun Res Inst Crawley WA 6009 Australia

The problem of designing a transmit pulse such that after transmission over a dispersive channel the received pulse fits in a prescribed template can be formulated as a quadratic programming problem with affine semi-infinite constraints. In constrained optimisation, the optimal solution invariably lies on the boundary of the feasible set, and consequently perturbations on the optimal solution or the constraints means that the received pulses may no longer fit in the template. Perturbations to the optimal transmit pulse and the constraints arise, in practice, from errors in the implementation and uncertainty in the channel parameter, respectively. In the paper, a robust formulation is presented which ensures that the constraints are satisfied even in the presence of implementation errors and channel parameter uncertainty. The technique developed is applied to determine the optimal transmit pulse shape to be programmed on a commercial T1 (1.544 MbiUs) line interface unit.

关键词： filtering theory quadratic programming dispersive channel line interface unit dispersive channels quadratic programming problem optimal transmit pulse shape perturbation techniques Filtering methods in signal processing Optimisation techniques affine semiinfinite constraints Signal processing theory robust transmit pulse design

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Computationally efficient model predictive control for a class of linear parameter-varying systems

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IET CONTROL THEORY AND APPLICATIONS 2018年第10期12卷 1384-1392页

作者： Cavanini, Luca Cimini, Gionata Ippoliti, Gianluca Univ Politecn Marche Dipartimento Ingn Informaz Via Brecce Bianche 12 I-60131 Ancona Italy ODYS Srl Milan Italy

The use of linear parameter varying (LPV) prediction models has been proven to be an effective solution to develop model predictive control (MPC) algorithms for linear and non-linear systems. However, the computational effort is a crucial issue for LPV-MPC, which has severely limited its application especially in embedded control. Indeed, for dynamical systems of dimension commonly found in embedded applications, the time needed to form the quadratic programming (QP) problem at each time step, can be substantially higher than the average time to solve it, making the approach infeasible in many control boards. This study presents an algorithm that drastically reduces this computational complexity for a particular class of LPV systems. They show that when the input matrix is right-invertible, the rebuild phase of the QP problem can be accelerated by means of a coordinate transformation which approximates the original formulation. Then they introduce a variant of the algorithm, able to further reduce this time, at the cost of a slightly increased sub-optimality. The presented results on vehicle dynamics and electrical motor control confirm the effectiveness of the two novel methods, especially in those applications where computational load is a key indicator for success.

关键词： time-varying systems vehicle dynamics machine control quadratic programming linear systems computational complexity control system synthesis predictive control electric motors effective solution model predictive control algorithms computational effort crucial issue LPV-MPC embedded control embedded applications quadratic programming problem average time control boards computational complexity LPV systems QP problem electrical motor control computational load linear parameter-varying systems computationally efficient model predictive control LPV prediction models vehicle dynamics

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Functional iterative approaches for solving support vector classification problems based on generalized Huber loss

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NEURAL COMPUTING & APPLICATIONS 2020年第13期32卷 9245-9265页

作者： Borah, Parashjyoti Gupta, Deepak Natl Inst Technol Arunachal Pradesh Dept Comp Sci & Engn Yupia India

Classical support vector machine (SVM) and its twin variant twin support vector machine (TWSVM) utilize the Hinge loss that shows linear behaviour, whereas the least squares version of SVM (LSSVM) and twin least squares support vector machine (LSTSVM) uses L-2-norm of error which shows quadratic growth. The robust Huber loss function is considered as the generalization of Hinge loss and L-2-norm loss that behaves like the quadratic L-2-norm loss for closer error points and the linear Hinge loss after a specified distance. Three functional iterative approaches based on generalized Huber loss function are proposed in this paper to solve support vector classification problems of which one is based on SVM, i.e. generalized Huber support vector machine and the other two are in the spirit of TWSVM, namely generalized Huber twin support vector machine and regularization on generalized Huber twin support vector machine. The proposed approaches iteratively find the solutions and eliminate the requirements to solve any quadratic programming problem (QPP) as for SVM and TWSVM. The main advantages of the proposed approach are: firstly, utilize the robust Huber loss function for better generalization and for lesser sensitivity towards noise and outliers as compared to quadratic loss;secondly, it uses functional iterative scheme to find the solution that eliminates the need to solving QPP and also makes the proposed approaches faster. The efficacy of the proposed approach is established by performing numerical experiments on several real-world datasets and comparing the result with related methods, viz. SVM, TWSVM, LSSVM and LSTSVM. The classification results are convincing.

关键词： Support vector machine Functional iterative scheme Huber loss function quadratic programming problem

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A mathematical programming model for computing the Fries number of a fullerene

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APPLIED MATHEMATICAL MODELLING 2015年第18期39卷 5473-5479页

作者： Salami, M. Ahmadi, M. B. Shiraz Univ Dept Math Coll Sci Shiraz Iran

A fullerene graph is a cubic 3-connected plane graph with pentagonal and hexagonal faces. The Fries number of a fullerene is the maximum number of benzene-like faces over all possible perfect matchings. The Fries number and its associated Kekule structure of a fullerene play a key role in molecular energy and stability. In this paper we propose a binary integer linear programming and a quadratic programming model for determining the Fries number of a fullerene. Moreover, interior point approach, as one of the most robust optimization techniques, is implemented to find the optimal solution of the proposed quadratic programming problem in moderate computing time. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Binary integer linear programming quadratic programming problem Perfect matching Fries number Fullerenes

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An improved constrained dynamic matrix control for temperature in an industrial coke furnace

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MEASUREMENT & CONTROL 2019年第5-6期52卷 409-417页

作者： Zou, Hongbo Wang, Limin Hangzhou Dianzi Univ Inst Informat & Control Hangzhou 310018 Zhejiang Peoples R China Hainan Normal Univ Sch Math & Stat Haikou Hainan Peoples R China

In order to derive the feasible control law of the constrained model predictive control scheme, quadratic programming has been introduced as an effective method. It is known that the typical performance index for model predictive control strategies under various constraints can be converted into a standard quadratic programming problem;however, there may be no feasible solutions for the corresponding quadratic programming problem when the working conditions are too bad or constraints are too rigorous, the real-time control law cannot be updated and the system performance may be deteriorated. To cope with such problems, an improved quadratic programming problem in which relaxations are employed to increase the possibility of successful solutions is proposed for the constrained dynamic matrix control approach in this paper. By adopting the introduced relaxations, more degrees of relaxations are provided for the optimization process under the case of over-constrained, such that the control law is easier to yield. Case study on the temperature regulation of the coke furnace demonstrates the validity of the improved quadratic programming structure-based dynamic matrix control strategy. Simulation results show that the proposed scheme yields improved control performance.

关键词： Dynamic matrix control quadratic programming problem relaxations constraints temperature regulation

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A dynamical model for solving degenerate quadratic minimax problems with constraints

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2011年第6期236卷 1282-1295页

作者： Nazemi, A. R. Shahrood Univ Technol Dept Math Sch Math Sci Shahrood Iran

This paper presents a new neural network model for solving degenerate quadratic minimax (DQM) problems. On the basis of the saddle point theorem, optimization theory, convex analysis theory, Lyapunov stability theory and LaSalle invariance principle, the equilibrium point of the proposed network is proved to be equivalent to the optimal solution of the DQM problems. It is also shown that the proposed network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the original problem. Several illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Neural network Dynamic system Minimax problem quadratic programming problem Convergent Stability

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Collocation-variation difference schemes with several collocation points for differential-algebraic equations

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APPLIED NUMERICAL MATHEMATICS 2020年 149卷 153-163页

作者： Bulatov, Mikhail Solovarova, Liubov RAS SB Matrosov Inst Syst Dynam & Control Theory Lermontov St 134 Irkutsk Russia

We consider the initial value problem in linear differential-algebraic equations. We propose collocation-variation difference schemes with several collocation points and show the principal difference between these approaches and the known difference schemes. Analysis of the particular cases of such schemes and calculations of the test examples are given. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Differential-algebraic equations Difference scheme quadratic programming problem Initial value problem

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Mean-variance optimal trading problem subject to stochastic dominance constraints with second order autoregressive price dynamics

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2017年第1期86卷 29-69页

作者： Singh, Arti Selvamuthu, Dharmaraja IIT Delhi Dept Math New Delhi 110016 India

The efficient modeling of execution price path of an asset to be traded is an important aspect of the optimal trading problem. In this paper an execution price path based on the second order autoregressive process is proposed. The proposed price path is a generalization of the existing first order autoregressive price path in literature. Using dynamic programming method the analytical closed form solution of unconstrained optimal trading problem under the second order autoregressive process is derived. However in order to incorporate non-negativity constraints in the problem formulation, the optimal static trading problems under second order autoregressive price process are formulated. For a risk neutral investor, the optimal static trading problem of minimizing expected execution cost subject to non-negativity constraints is formulated as a quadratic programming problem. Whereas, for a risk averse investor the variance of execution cost is considered as a measure for the timing risk, and the mean-variance problem is formulated. Moreover, the optimal static trading problem subject to stochastic dominance constraints with mean-variance static trading strategy as the reference strategy is studied. Using Static approximation method the algorithm to solve proposed optimal static trading problems is presented. With numerical illustrations conducted on simulated data and the real market data, the significance of second order autoregressive price path, and the optimal static trading problems is presented.

关键词： Optimal trading Execution cost Stochastic dominance Autoregressive behavior quadratic programming problem Risk averse

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