• Title, Summary, Keyword: nonlinear problems

Search Result 1,316, Processing Time 0.032 seconds

A Nonlinear Programming Approach to Biaffine Matrix Inequality Problems in Multiobjective and Structured Controls

  • Lee, Joon-Hwa;Lee, Kwan-Ho;Kwon, Wook-Hyun
    • International Journal of Control, Automation, and Systems
    • /
    • v.1 no.3
    • /
    • pp.271-281
    • /
    • 2003
  • In this paper, a new nonlinear programming approach is suggested to solve biaffine matrix inequality (BMI) problems in multiobjective and structured controls. It is shown that these BMI problems are reduced to nonlinear minimization problems. An algorithm that is easily implemented with existing convex optimization codes is presented for the nonlinear minimization problem. The efficiency of the proposed algorithm is illustrated by numerical examples.

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

  • Kim, Sun-Young
    • Communications of the Korean Mathematical Society
    • /
    • v.11 no.4
    • /
    • pp.1147-1157
    • /
    • 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.

  • PDF

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
    • /
    • v.15 no.1
    • /
    • pp.73-82
    • /
    • 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.

  • PDF

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

  • Song, Hwachang
    • International Journal of Fuzzy Logic and Intelligent Systems
    • /
    • v.13 no.3
    • /
    • pp.171-177
    • /
    • 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.

LOCAL EXISTENCE AND GLOBAL UNIQUENESS IN ONE DIMENSIONAL NONLINEAR HYPERBOLIC INVERSE PROBLEMS

  • Choi, Jong-Sung
    • Communications of the Korean Mathematical Society
    • /
    • v.17 no.4
    • /
    • pp.593-606
    • /
    • 2002
  • We prove local existence and global uniqueness in one dimensional nonlinear hyperbolic inverse problems. The basic key for showing the local existence of inverse solution is the principle of contracted mapping. As an application, we consider a hyperbolic inverse problem with damping term.

On the regularization with nonlinear splines

  • Chung, S.K.;Joe, S.M.
    • Communications of the Korean Mathematical Society
    • /
    • v.12 no.1
    • /
    • pp.165-176
    • /
    • 1997
  • In order to overcome computational ill-posedness which arises when we solve the least square problems, nonlinear smoothing splines are used. The existence and the convergence on nonlinear smoothing spline are shown with numerical experiments.

  • PDF

A NEWTON-IMPLICIT ITERATIVE METHOD FOR NONLINEAR INVERSE PROBLEMS

  • Meng, Zehong;Zhao, Zhenyu
    • Journal of applied mathematics & informatics
    • /
    • v.29 no.3_4
    • /
    • pp.909-920
    • /
    • 2011
  • A regularized Newton method for nonlinear ill-posed problems is considered. In each Newton step an implicit iterative method with an appropriate stopping rule is proposed and analyzed. Under certain assumptions on the nonlinear operator, the convergence of the algorithm is proved and the algorithm is stable if the discrepancy principle is used to terminate the outer iteration. Numerical experiment shows the effectiveness of the method.

A pole assignment control design for single-input double-output nonlinear mechanical systems

  • Kobayashi, Masahito;Tamura, Katsutoshi
    • 제어로봇시스템학회:학술대회논문집
    • /
    • /
    • pp.144-149
    • /
    • 1993
  • This paper discusses a design of a nonlinear control for a class of single-input double-output nonlinear mechanical systems. When conventional linearization methods are applied to the mechanical systems, some problems of oscillation and unstable phenomena arise. The proposed nonlinear control system resolves these problems. In this design the eigenvalues of the closed-loop nonlinear system are assigned to desired locations and local asymptotic stability of the closed-loop system. is guaranteed. The design method is applied to an inverted pendulum system with a moving weight mechanism. Experimental results show that the proposed nonlinear controller is more effective for stability than the usual linear controller.

  • PDF

EXISTENCE OF SOLUTIONS OF NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS FOR 2NTH-ORDER NONLINEAR DIFFERENTIAL EQUATION

  • Gao, Yongxin;Wang, Renfei
    • Journal of applied mathematics & informatics
    • /
    • v.27 no.5_6
    • /
    • pp.1465-1472
    • /
    • 2009
  • In This paper we shall study the existence of solutions of nonlinear two point boundary value problems for nonlinear 2nth-order differential equation $y^{(2n)}=f(t,y,y',{\cdots},y^{(2n-1)})$ with the boundary conditions $g_0(y(a),y'(a),{\cdots},y^{2n-3}(a))=0,g_1(y^{(2n-2)}(a),y^{(2n-1)}(a))=0$, $h_o(y(c),y'(c))=0,h_i(y^{(i)}(c),y^{(i+1)}(c))=0(i=2,3,{\cdots},2n-2)$.

  • PDF

On Strongly Nonlinear Implicit Complementarity Problems in Hilbert Spaces

  • Cho, Yeol Je;Huang, Nan-Jing
    • Kyungpook Mathematical Journal
    • /
    • v.46 no.1
    • /
    • pp.145-152
    • /
    • 2006
  • In this paper, we study a class of strongly nonlinear implicit complementarity problems in the setting of Hilbert spaces H (not necessarily Hilbert lattices). By using the property of the projection and a suitable change of variables, we establish the equivalence between the strongly nonlinear implicit complementarity problem and the fixed point problem in H. Moreover, we use this equivalence and the fixed point theorem of Boyd and Wong to prove the existence and uniqueness of solutions for the strongly nonlinear implicit complementarity problem in H.

  • PDF