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quadratic programming problems and Its Solution Techniques With Neural Network Modeling

OPTIMAL CONTROL APPLICATIONS & METHODS 2025年第2期46卷 766-774页

作者： Sah, Mintu Kumar Varma, Neha Kumar, Sanjay Lalit Narayan Mithila Univ Univ Dept Math Darbhanga India Amity Univ Patna Amity Sch Engn & Technol Patna India

This paper presents a study on quadratic programming problems (QPP) and introduces a new neural network model with feasibility analysis. The stability analysis of QPP using neural network modeling is also discussed. The proposed neural network model has a simple form, and its optimal feasibility for both primal and dual QP problems is established. The model demonstrates a good convergence rate with a minimal number of iterations, achieving a very fast convergence to the exact solutions of both the primal and dual QP problems. The optimal solutions for the original QP problem and its dual QPP are obtained. Finally, two simple numerical examples are simulated to illustrate the findings.

关键词： neural network quadratic programming problems stability analysis

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Optimizing quadratic programming problems with intuitionistic fuzzy parameters using a neural network

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2025年 151卷

作者： Rani, Pooja Mahajan, Sumati Punjab Engn Coll Dept Math Chandigarh 160012 India

The integration of intuitionistic fuzzy theory in optimization problems has significantly enhanced the ability to handle complex, uncertain and imprecise scenarios. Despite these advancements, existing models have not adequately addressed the specific challenges of intuitionistic fuzzy quadratic programming problems (IFQPPs). This study fills this gap by proposing a novel recurrent neural network for IFQPPs. First of all, IFQPP is transformed into a multi-objective optimization problem using alpha, /3-cuts. This technique allows to explore a wide range of possible solutions using various combinations of alpha, /3-cuts. Next, the multi-objective problem is converted into a weighted problem coupled with duality theory to remodel into a single-layer recurrent neural network. To validate the proposed approach, theorems as well as lemmas have been constructed and proved at appropriate places. The proposed neural network model is illustrated using numerical examples to explain the methodology. Later, it is applied to a small-scale electrical power grid to demonstrate the practical utility and impact of the proposed approach.

关键词： Neural network Intuitionistic fuzzy parameters quadratic programming problems a,/3-cut

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An improved multi-task least squares twin support vector machine

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ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE 2025年第1期93卷 21-41页

作者： Moosaei, Hossein Bazikar, Fatemeh Pardalos, Panos M. M. Jan Evangelista Purkyne Univ Usti Nad Labem Fac Sci Dept Informat Usti Nad Labem Czech Republic Univ Bojnord Dept Math Bojnord Iran Univ Guilan Fac Math Sci Dept Appl Math Rasht Iran Univ Florida Ctr Appl Optimizat Dept Ind & Syst Engn Gainesville FL 32611 USA

In recent years, multi-task learning (MTL) has become a popular field in machine learning and has a key role in various domains. Sharing knowledge across tasks in MTL can improve the performance of learning algorithms and enhance their generalization capability. A new approach called the multi-task least squares twin support vector machine (MTLS-TSVM) was recently proposed as a least squares variant of the direct multi-task twin support vector machine (DMTSVM). Unlike DMTSVM, which solves two quadratic programming problems, MTLS-TSVM solves two linear systems of equations, resulting in a reduced computational time. In this paper, we propose an enhanced version of MTLS-TSVM called the improved multi-task least squares twin support vector machine (IMTLS-TSVM). IMTLS-TSVM offers a significant advantage over MTLS-TSVM by operating based on the empirical risk minimization principle, which allows for better generalization performance. The model achieves this by including regularization terms in its objective function, which helps control the model's complexity and prevent overfitting. We demonstrate the effectiveness of IMTLS-TSVM by comparing it to several single-task and multi-task learning algorithms on various real-world data sets. Our results highlight the superior performance of IMTLS-TSVM in addressing multi-task learning problems.

关键词： Least squares Multi-task learning Twin support vector machine Multi-task twin support vector machine quadratic programming problems

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Quasi-Newton approaches to interior point methods for quadratic problems

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2019年第1期74卷 93-120页

作者： Gondzio, J. Sobral, F. N. C. Univ Edinburgh Sch Math Edinburgh EH9 3FD Midlothian Scotland Univ Estadual Maringa Dept Math Ave Colombo 5790 BR-87020900 Maringa Parana Brazil

Interior point methods (IPM) rely on the Newton method for solving systems of nonlinear equations. Solving the linear systems which arise from this approach is the most computationally expensive task of an interior point iteration. If, due to problem's inner structure, there are special techniques for efficiently solving linear systems, IPMs demonstrate a reduced computing time and are able to solve large scale optimization problems. It is tempting to try to replace the Newton method by quasi-Newton methods. Quasi-Newton approaches to IPMs either are built to approximate the Lagrangian function for nonlinear programming problems or provide an inexpensive preconditioner. In this work we study the impact of using quasi-Newton methods applied directly to the nonlinear system of equations for general quadratic programming problems. The cost of each iteration can be compared to the cost of computing correctors in a usual interior point iteration. Numerical experiments show that the new approach is able to reduce the overall number of matrix factorizations.

关键词： Broyden method Quasi-Newton Interior point methods quadratic programming problems

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Throttle Valve Control of Automotive Engine based on Boundary Model

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IFAC-PapersOnLine 2018年第13期51卷 143-148页

作者： Sato, K. Sadahiro, T. Yamazaki, M. Iwase, M. Department of Robotics and Mechatronics Tokyo Denki University 5 Senju-Asahicho AdachiTokyo120-8551 Japan Department of Mechanical Engineering National Institute of Technology Sasebo College 1-1 Okishin-machi SaseboNagasaki857-1193 Japan

The purpose of this research is to control the automotive engine inside the boundary between the admissible operation domain and the violated admissible operation domain. “Model Following Control” to follow the driver's requirement and “Near Boundary Control” along the boundary are realized by optimization control by a quadratic programming problem in which “Control Lyapunov Function” and “Control Barrier Function” are combined. The operation of the proposed control method was confirmed on a numerical simulation. As a result of the simulation, the proposed method was confirmed to control the automotive engine within the admissible operation domain. © 2018

关键词： Automobile engines Lyapunov functions Lyapunov methods Numerical methods quadratic programming Automotive engine Boundary controls Boundary models Control barriers Control Lyapunov function Model following control Optimization control quadratic programming problems

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Recursive Subspace-based Predictive Control and Its Application to Fault-tolerant Control

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IFAC-PapersOnLine 2018年第24期51卷 696-702页

作者： Gao, Jingjing Yang, Xu Li, Linlin Luo, Hao Ding, Steven X. Zhang, Kai Peng, Kaixiang School of Automation and Electrical Engineering University of Science and Technology Beijing Beijing100083 China School of Astronautics Harbin Institute of Technology Harbin150001 China Institute of Automatic Control and Complex Systems Faculty of Engineering University of Duisburg-Essen Duisburg47057 Germany

This paper investigates the data-driven realization of predictive controllers, and its application to fault-tolerant control. With the aid of subspace identification method, the subspace predictor is first derived in the closed-loop setup. To cope with the change in the process, a recursive algorithm is adopted to recursive update the subspace matrices. The data-driven predictive controller is designed by seeking the solution of the quadratic programming problem, without the information of the predesigned controller. Then, it is applied to fault-tolerant control by implementing the recursive subspace predictor. In the end, the effectiveness of the proposed method is verified by a case study on the three-tank system. © 2018

关键词： Controllers Fault tolerance quadratic programming Fault tolerant control Predictive control Predictive controller quadratic programming problems Recursive algorithms Subspace identification methods Subspace predictors Three tank system

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Fast Sensitivity-Based Nonlinear Economic Model Predictive Control with Degenerate NLP

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IFAC-PapersOnLine 2018年第18期51卷 399-404页

作者： Suwartadi, Eka Jäschke, Johannes Trondheim7491 Norway

We present a fast sensitivity-based nonlinear model predictive control (NMPC) algorithm, that can handle non-unique multipliers in the discretized dynamic optimization problem. Non-unique multipliers may arise, for example when path constraints are active for longer periods of the prediction horizon. This is a common situation in economic model predictive control. In such cases, the optimal nonlinear programming (NLP) solution often satisfies the Mangasarian-Fromovitz constraint qualification (MFCQ), which implies non-unique, but bounded multipliers. Consequently, any sensitivity-based fast NMPC scheme must allow for discontinuous jumps in the multipliers. In this paper, we apply a sensitivity-based path-following algorithm that allows multiplier jumps within the advance-step NMPC (asNMPC) framework. The path-following method consists of a corrector and a predictor step, which are computed by solving a system of linear equations, and a quadratic programming problem, respectively, and a multiplier jump step determined by the solution of a linear program. We demonstrate the proposed method on an economic NMPC case study with a CSTR. © 2018

关键词： Model predictive control Linear programming Predictive control systems quadratic programming Dynamic optimization problem (DOP) Economic modeling Nonlinear model predictive control Optimal controls Parametric optimization Path following quadratic programming problems System of linear equations

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Eigenvalue analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB

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APPLIED MATHEMATICAL MODELLING 2017年 49卷 680-690页

作者： Li, Qi Qiu, Zhiping Zhang, Xudong Chinese Acad Sci Shenyang Inst Automat State Key Lab Robot Shenyang 110016 Peoples R China Beijing Univ Aeronaut & Astronaut Inst Solid Mech Beijing Peoples R China Beijing Aerosp Technol Inst Beijing Peoples R China

When the uncertainties in interval parameters are fairly large, the current analysis methods, which are usually based on the information of the first-order partial derivatives of eigenvalues, may not work well for the structural eigenvalue problem with interval parameters. To overcome this drawback, in this work, the structural eigenvalue problem with interval parameters is modeled as a series of QB (quadratic programming with box constrains) problems by taking advantage of the information of the second-order partial derivatives of eigenvalues. Then the series of QB problems would be solved by using the DCA (difference of convex functions algorithm) which is turn out be very effective for the QB problem. The specific examples, a concrete frame with sixty bars and a plate discretized with 300 finite elements, are given to show the effectiveness and feasibility of the proposed method compared with other methods. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Interval parameters Second-order Taylor series expansion Eigenvalues of uncertain structures quadratic programming problems DCA

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On a conjugate directions method for solving strictly convex QP problem

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2017年第3期86卷 523-548页

作者： Stachurski, Andrzej Warsaw Univ Technol Inst Control & Computat Engn Nowowiejska 15-19 PL-00665 Warsaw Poland

Problem of solving the strictly convex, quadratic programming problem is studied. The idea of conjugate directions is used. First we assume that we know the set of directions conjugate with respect to the hessian of the goal function. We apply n simultaneous directional minimizations along these conjugate directions starting from the same point followed by the addition of the directional corrections. Theorem justifying that the algorithm finds the global minimum of the quadratic goal function is proved. The way of effective construction of the required set of conjugate directions is presented. We start with a vector with zero value entries except the first one. At each step new vector conjugate to the previously generated is constructed whose number of nonzero entries is larger by one than in its predecessor. Conjugate directions obtained by means of the above construction procedure with appropriately selected parameters form an upper triangular matrix which in exact computations is the Cholesky factor of the inverse of the hessian matrix. Computational cost of calculating the inverse factorization is comparable with the cost of the Cholesky factorization of the original second derivative matrix. Calculation of those vectors involves exclusively matrix/vector multiplication and finding an inverse of a diagonal matrix. Some preliminary computational results on some test problems are reported. In the test problems all symmetric, positive definite matrices with dimensions from to from the repository of the Florida University were used as the hessians.

关键词： Conjugate directions quadratic programming problems Distributed calculations

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Low Complexity Distributed Model Predictive Control by Using Contractive Sets

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IFAC-PapersOnLine 2017年第1期50卷 13164-13169页

作者： Grancharova, Alexandra Olaru, Sorin Department of Industrial Automation University of Chemical Technology and Metallurgy Bul. Kl. Ohridski 8 Sofia1756 Bulgaria Laboratory of Signals and Systems CentraleSupélec-CNRS-Université Paris-Sud Université Paris-Saclay 3 Rue Joliot-Curie Gifsur-Yvette Cedex91192 France

In this paper, an approach to low complexity distributed MPC of linear interconnected systems with coupled dynamics subject to both state and input constraints is proposed. The suggested approach is based on the idea of introducing a contractive set constraint in the centralized MPC problem formulation, which would guarantee the closed-loop system stability when using a small prediction horizon. Then, a dual accelerated gradient method is applied to obtain distributedly a suboptimal solution of the resulting quadratic programming problem. The suggested approach would be appropriate for embedded distributed MPC since it will reduce the complexity of the on-line MPC computations, simplify the software implementation, and reduce the requirements for available memory. © 2017

关键词： Predictive control systems Closed loop systems Distributed parameter control systems Gradient methods Large scale systems Linear systems Model predictive control quadratic programming System stability Constraints Distributed control Distributed Model predictive Control Predictive control Problem formulation quadratic programming problems Software implementation State and input constraints

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