Presented is a general method for solving sets of nonlinear constraints that include inequalities. Inequality constraints are common in engineering design problems, such as kinematic synthesis. The proposed method uses a modified Newton’s method and introduces a slack variable and a slack constraint to convert each inequality into an equality constraint. Singular value decomposition is used to find the pseudo-inverse of the Jacobian at each iteration. Benefits of this method are that constraint scaling is not an issue and that the method often fails gracefully for inconsistent constraint sets by providing direction for modification of the constraints so that an answer can be found. The method is also competitive with others in terms of the number of function evaluations needed to solve a set of problems taken from the literature.
A New Method for Solving Mixed Sets of Equality and Inequality Constraints
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Mullins, S. H., Charlesworth, W. W., and Anderson, D. C. (June 1, 1995). "A New Method for Solving Mixed Sets of Equality and Inequality Constraints." ASME. J. Mech. Des. June 1995; 117(2A): 322–328. https://doi.org/10.1115/1.2826142
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