Abstract
An iterative technique is developed to solve the problem of minimizing a functionf(y) subject to certain nonlinear constraintsg(y)=0. The variables are separated into the basic variablesx and the independent variablesu. Each iteration consists of a gradient phase and a restoration phase. The gradient phase involves a movement (on a surface that is linear in the basic variables and nonlinear in the independent variables) from a feasible point to a varied point in a direction based on the reduced gradient. The restoration phase involves a movement (in a hyperplane parallel tox-space) from the nonfeasible varied point to a new feasible point.
The basic scheme is further modified to implement the method of conjugate gradients. The work required in the restoration phase is considerably reduced when compared with the existing methods.
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Communicated by D. G. Luenberger
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Mikkilineni, R.P., Feagin, T. A computational method for minimization with nonlinear constraints. J Optim Theory Appl 25, 335–347 (1978). https://doi.org/10.1007/BF00932897
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DOI: https://doi.org/10.1007/BF00932897