Bifurcation and Persistance of Minima in Nonlinear Parametric Programming

  • C. A. Tiahrt
  • A. B. Poore
Part of the Progress in Systems and Control Theory book series (PSCT, volume 1)


In this paper, the structure of solutions to the nonlinear parametric programming problem
$$\min \{ {\text{f(x,}}\alpha {\text{):h(x,}}\alpha {\text{) = 0,g(x,}}\alpha {\text{)}} \geqslant {\text{0\} }}$$
is studied as the parameter α ∈ Rvaries. Here f: R n+1R, g: R n+1R p , h: R n+1R q will be assumed at least twice continuously differentiable. Both the bifurcation of curves of critical points and the persistance of minima along these curves will be examined. There has been considerable recent interest [1,4,5,8,10–13,16,17,19–25] in this problem, stemming from the solution of parameter-free optimization problems by homotopy methods, from multi-objective optimization, and from applications requiring a parametric analysis of sensitivity and stability.


Tangent Space Bifurcation Theory Parametric Program Linear Independence Constraint Qualification Linear Parametric Program 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Birkhäuser Boston 1989

Authors and Affiliations

  • C. A. Tiahrt
    • 1
  • A. B. Poore
    • 2
  1. 1.Deptartment of Mathematics adn StatisticsUniversity of Nebraska - LincolnLincolnUSA
  2. 2.Department of MathematicsColorado State UniversityFort CollinsUSA

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