Starting from one extension of the Hahn-Banach theorem, the Mazur-Orlicz theorem, and a not very restrictive concept of convexity, that arises naturally in minimax theory, infsup-convexity, we derive an equivalent ver...
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Starting from one extension of the Hahn-Banach theorem, the Mazur-Orlicz theorem, and a not very restrictive concept of convexity, that arises naturally in minimax theory, infsup-convexity, we derive an equivalent version of that fundamental result for finite dimensional spaces, which is a sharp generalization of Konig's Maximum theorem. It implies several optimal statements of the Lagrange multipliers, Karush/Kuhn-Tucker, and Fritz John type for nonlinear programs with an objective function subject to both equality and inequality constraints.
Methods are considered for solving nonlinear programming problems using an exactl 1 penalty function. LP-like subproblems incorporating a trust region constraint are solved successively both to estimate the active set...
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Methods are considered for solving nonlinear programming problems using an exactl 1 penalty function. LP-like subproblems incorporating a trust region constraint are solved successively both to estimate the active set and to provide a foundation for proving global convergence. In one particular method, second order information is represented by approximating the reduced Hessian matrix, and Coleman-Conn steps are taken. A criterion for accepting these steps is given which enables the superlinear convergence properties of the Coleman-Conn method to be retained whilst preserving global convergence and avoiding the Maratos effect. The methods generalize to solve a wide range of composite nonsmooth optimization problems and the theory is presented in this general setting. A range of numerical experiments on small test problems is described.
A model algorithm based on the successive quadratic programming method for solving the general nonlinear programming problem is presented. The objective function and the constraints of the problem are only required to...
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A model algorithm based on the successive quadratic programming method for solving the general nonlinear programming problem is presented. The objective function and the constraints of the problem are only required to be differentiable and their gradients to satisfy a Lipschitz condition. The strategy for obtaining global convergence is based on the trust region approach. The merit function is a type of augmented Lagrangian. A new updating scheme is introduced for the penalty parameter, by means of which monotone increase is not necessary. Global convergence results are proved and numerical experiments are presented.
We propose an approach for multi-attribute group decision-making (MAGDM) problems under neutrosophic information, where the preference values of alternatives over the attributes and the importance of attributes are ex...
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We propose an approach for multi-attribute group decision-making (MAGDM) problems under neutrosophic information, where the preference values of alternatives over the attributes and the importance of attributes are expressed in terms of single-valued neutrosophic sets. Firstly, we develop a nonlinear programming approach based on Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method to determine relative closeness intervals of alternatives. Secondly, we aggregate closeness intervals to find out the ranking order of all alternatives by computing their optimal membership degrees based on the ranking method of interval numbers. Finally, we provide an illustrative example to show the effectiveness of the proposed approach.
We explore properties of nonlinear programming problems (NLPs) that arise in the formulation of NMPC subproblems and show their influence on stability and robustness of NMPC. NLPs that satisfy linear independence cons...
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We explore properties of nonlinear programming problems (NLPs) that arise in the formulation of NMPC subproblems and show their influence on stability and robustness of NMPC. NLPs that satisfy linear independence constraint qualification (LICQ), second order sufficient conditions (SOSC) and strict complementarity (SC), have solutions that are continuous and differentiable with perturbations of the problem data. As a result, they are important prerequisites for nominal and ISS stability of NMPC controllers. Moreover, we show that ensuring these properties is possible through reformulation of the NLP subproblem for NMPC, through the addition of (1 penalty and barrier terms. We show how these properties also establish ISS of related sensitivity-based NMPC controllers, such as asNMPC and amsNMPC. Finally, we demonstrate the impact of our reformulated NLPs on several examples that have shown nonrobust performance on earlier NMPC strategies. (C) 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
The polyester fiber spinning process is extensive, and the involved dynamic models are complex and difficult to solve analytically. This paper presents the optimal control strategy of polyester fiber production. Based...
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ISBN:
(纸本)9781665478960
The polyester fiber spinning process is extensive, and the involved dynamic models are complex and difficult to solve analytically. This paper presents the optimal control strategy of polyester fiber production. Based on a dynamic model of the spinning process, optimal objectives are determined to minimize production costs and meet production goals. We employ Radau collocation on finite elements to discretize the continuous dynamic model, which is transformed into finite-dimensional nonlinear programming (NLP) model. The developed strategy combines a multiple shot algorithm and half-score method to solve the obtained NLP model. We find the best initial values quickly and achieve the control objective under the constraints of the spinning process's mechanism equations. The objective function measures the difference between the actual production and the desired value, and the merit of the objective function directly affects the control variables. In this paper, single-objective and multi-objective control strategies are designed according to different production requirements. To make the objective function effectively reflect the product quality, its setting is inseparable from each state variable, and we explore the control effect for different objective functions. Finally, simulation results verify the feasibility and superiority of the orthogonal collocation on finite element and multiple shooting algorithms.
In recent years, the workload of healthcare workers in hospitals has increased, and there has been a demand for autonomous patrolling instead of nurses and gait measurements of patients in hospital wards. In this stud...
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ISBN:
(数字)9783031448515
ISBN:
(纸本)9783031448508;9783031448515
In recent years, the workload of healthcare workers in hospitals has increased, and there has been a demand for autonomous patrolling instead of nurses and gait measurements of patients in hospital wards. In this study, a novel motion-planning method is proposed to enable a mobile robot to measure the gait of passing pedestrians while patrolling wards. In nonlinear programming, the feasibility of the gait measurement is evaluated as an object function, and constraints on the robot kinematics, environment, collision avoidance, and target position and arrival time are considered in the constraints. The optimization variables are the trajectory of the robot's position, velocity, and acceleration. This schematization guarantees that the control input, which is the solution to this problem, satisfies all constraints and is optimized to realize gait measurement. The results of the simulation and experiment demonstrated the efficiency and evolvability of the proposed method.
The purpose of this paper is to develop a nonlinear programming method for solving a type of cooperative games in which there are multiple objectives and coalitions' values on objectives are expressed with interva...
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ISBN:
(纸本)9781479944675
The purpose of this paper is to develop a nonlinear programming method for solving a type of cooperative games in which there are multiple objectives and coalitions' values on objectives are expressed with intervals, which are called interval-valued multiobjective cooperative games for short. In this method, we define the concepts of interval-valued cores of interval-valued multiobjective cooperative games and satisfactory degrees of comparing intervals with inclusion and/or overlap relations. The interval-valued cores can be computed by developing a new two-phase method based on the auxiliary nonlinear programming models. The proposed method can seek cooperative chances under the situations of inclusion and/or overlap relations of intervals in which the traditional interval ranking method may not always assure that the interval-valued cores exist. The feasibility and applicability of the developed method are illustrated with a real example.
Maximum likelihood (ML) detection problems for several multiuser systems result in nonlinear optimization problems with unacceptably high complexity! One way of achieving near-optimum performance without the complexit...
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ISBN:
(纸本)0769510620
Maximum likelihood (ML) detection problems for several multiuser systems result in nonlinear optimization problems with unacceptably high complexity! One way of achieving near-optimum performance without the complexity associated with the ML detector is using nonlinear programming relaxations to approximate the solution of the ML detection problem at hand. Using this approach, new detectors are formulated and it is observed that some popular suboptimum receivers correspond to relaxations of the ML detectors. We concentrate on two types of systems to demonstrate this concept and evaluate the performance of the resulting detectors.
Auxiliary components in some systems exist only to serve some other primary components. Preventive Maintenance (PM) activities are, therefore, done to these auxiliary components for the sake of extending the life of t...
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ISBN:
(纸本)9781424415281
Auxiliary components in some systems exist only to serve some other primary components. Preventive Maintenance (PM) activities are, therefore, done to these auxiliary components for the sake of extending the life of the primary component. Frequent PM care to auxiliary components increase the cost of PM while infrequent PM leads to increasing downtime of the primary component and, subsequently, production losses. The search for the optimal level of PM care requires a non-linear programming (NLP) solution that can, sometimes, be very complex. This paper suggests that a very useful pattern exists in the NLP model of this optimization problem which can significantly reduce the complexity of model formulation and the arrival to the NLP solution.
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