• Title/Summary/Keyword: Nonlinear constraints

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Fuzzy-Enforced Complementarity Constraints in Nonlinear Interior Point Method-Based Optimization

  • Song, Hwachang
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.13 no.3
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    • pp.171-177
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    • 2013
  • This paper presents a fuzzy set method to enforce complementarity constraints (CCs) in a nonlinear interior point method (NIPM)-based optimization. NIPM is a Newton-type approach to nonlinear programming problems, but it adopts log-barrier functions to deal with the obstacle of managing inequality constraints. The fuzzy-enforcement method has been implemented for CCs, which can be incorporated in optimization problems for real-world applications. In this paper, numerical simulations that apply this method to power system optimal power flow problems are included.

A Method using Parametric Approach for Constrained Optimization and its Application to a System of Structural Optimization Problems (제약을 갖는 최적화문제에 대한 파라메트릭 접근법과 구조문제의 최적화에 대한 응용)

  • Yang, Y.J.;Kim, W.S.
    • Journal of the Korean Operations Research and Management Science Society
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    • v.15 no.1
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    • pp.73-82
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    • 1990
  • This paper describes two algorithms to Nonlinear programming problems with equality constraints and with equality and inequality constraints. The first method treats nonlinear programming problems with equality constraints. Utilizing the nonlinear programming problems with equality constraints. Utilizing the nonlinear parametric programming technique, the method solves the problem by imbedding it into a suitable one-parameter family of problems. The second method is to solve a nonlinear programming problem with equality and inequality constraints, by minimizing a square sum of nonlinear functions which is derived from the Kuhn-Tucker condition.

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Trajectory Planning of Satellite Formation Flying using Nonlinear Programming and Collocation

  • Lim, Hyung-Chu;Bang, Hyo-Choong
    • Journal of Astronomy and Space Sciences
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    • v.25 no.4
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    • pp.361-374
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    • 2008
  • Recently, satellite formation flying has been a topic of significant research interest in aerospace society because it provides potential benefits compared to a large spacecraft. Some techniques have been proposed to design optimal formation trajectories minimizing fuel consumption in the process of formation configuration or reconfiguration. In this study, a method is introduced to build fuel-optimal trajectories minimizing a cost function that combines the total fuel consumption of all satellites and assignment of fuel consumption rate for each satellite. This approach is based on collocation and nonlinear programming to solve constraints for collision avoidance and the final configuration. New constraints of nonlinear equality or inequality are derived for final configuration, and nonlinear inequality constraints are established for collision avoidance. The final configuration constraints are that three or more satellites should form a projected circular orbit and make an equilateral polygon in the horizontal plane. Example scenarios, including these constraints and the cost function, are simulated by the method to generate optimal trajectories for the formation configuration and reconfiguration of multiple satellites.

A Least Squares Iterative Method For Solving Nonlinear Programming Problems With Equality Constraints

  • Sok Yong U.
    • Journal of the military operations research society of Korea
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    • v.13 no.1
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    • pp.91-100
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    • 1987
  • This paper deals with an algorithm for solving nonlinear programming problems with equality constraints. Nonlinear programming problems are transformed into a square sums of nonlinear functions by the Lagrangian multiplier method. And an iteration method minimizing this square sums is suggested and then an algorithm is proposed. Also theoretical basis of the algorithm is presented.

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CONVERGENCE ANALYSIS OF A NONLINEAR LAGRANGIAN ALGORITHM FOR NONLINEAR PROGRAMMING WITH INEQUALITY CONSTRAINTS

  • Zhang, Li-Wei;Liu, Yong-Jin
    • Journal of applied mathematics & informatics
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    • v.13 no.1_2
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    • pp.1-10
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    • 2003
  • In this paper, we establish a nonlinear Lagrangian algorithm for nonlinear programming problems with inequality constraints. Under some assumptions, it is proved that the sequence of points, generated by solving an unconstrained programming, convergents locally to a Kuhn-Tucker point of the primal nonlinear programming problem.

Nonlinear Programming Circuit using Neural Networks (신경회로망을 이용한 비선형 프로그래밍회로)

  • 강민제
    • Journal of the Institute of Convergence Signal Processing
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    • v.2 no.4
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    • pp.77-84
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    • 2001
  • Since Hopfield introduced the neural network for liner programming problems many papers have been published about it and some of them are about nonlinear programming problems Therefore nonlinear, cost function problem has been solved however nonlinear constraints problem has not been solved In this paper I have proposed the general nonlinear programming neural networks which minimize cost function with nonlinear constraints.

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Nonlinear Control of an Input-Constrained Inverted Pendulum (입력제약을 고려한 도립진자의 비선형 제어)

  • Jung, Jae-Hoon
    • Proceedings of the KIEE Conference
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    • 2003.11b
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    • pp.119-122
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    • 2003
  • The aim of this paper is to propose a nonlinear controller for a single cart-type inverted pendulum using energy-based control scheme. Using a nonlinear model relating the angular position and velocity to the control input and a nonlinear controller is designed to regulate the angular position and velocity in the presence of input constraints. It is proved that the angular position and velocity converge to zero.

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NUMERICAL METHDS USING TRUST-REGION APPROACH FOR SOLVING NONLINEAR ILL-POSED PROBLEMS

  • Kim, Sun-Young
    • Communications of the Korean Mathematical Society
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    • v.11 no.4
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    • pp.1147-1157
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    • 1996
  • Nonlinear ill-posed problems arise in many application including parameter estimation and inverse scattering. We introduce a least squares regularization method to solve nonlinear ill-posed problems with constraints robustly and efficiently. The regularization method uses Trust-Region approach to handle the constraints on variables. The Generalized Cross Validation is used to choose the regularization parameter in computational tests. Numerical results are given to exhibit faster convergence of the method over other methods.

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Neural Networks for Optimization Problem with Nonlinear Constraints (비선형제한조건을 갖는 최적화문제 신경회로망)

  • Kang, Min-Je
    • Journal of the Korean Institute of Intelligent Systems
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    • v.12 no.1
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    • pp.1-6
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    • 2002
  • Hopfield introduced the neural network for linear program with linear constraints. In this paper, Hopfield neural network has been generalized to solve the optimization problems including nonlinear constraints. Also, it has been discussed the methods hew to reconcile optimization problem with neural networks and how to implement the circuits.

Nonlinear Optimal Control of an Input-Constrained and Enclosed Thermal Processing System

  • Gwak, Kwan-Woong;Masada, Glenn Y.
    • International Journal of Control, Automation, and Systems
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    • v.6 no.2
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    • pp.160-170
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    • 2008
  • Temperature control of an enclosed thermal system which has many applications including Rapid Thermal Processing (RTP) of semiconductor wafers showed an input-constraint violation for nonlinear controllers due to inherent strong coupling between the elements [1]. In this paper, a constrained nonlinear optimal control design is developed, which accommodates input constraints using the linear algebraic equivalence of the nonlinear controllers, for the temperature control of an enclosed thermal process. First, it will be shown that design of nonlinear controllers is equivalent to solving a set of linear algebraic equations-the linear algebraic equivalence of nonlinear controllers (LAENC). Then an input-constrained nonlinear optimal controller is designed based on that LAENC using the constrained linear least squares method. Through numerical simulations, it is demonstrated that the proposed controller achieves the equivalent performances to the classical nonlinear controllers with less total energy consumption. Moreover, it generates the practical control solution, in other words, control solutions do not violate the input-constraints.