A first order, exact penalty function algorithm for equality constrained optimization problems

A first order algorithm for solving the problem of minimizing a function subject to equality constraints is presented. At each iteration the algorithm generates a search direction which has two components, the first component being chosen to satisfy (to first order) the equality constraint and the second to be a descent direction for the objective function. The step length is determined using an exact penalty function. A procedure for choosing a suitable value for the parameter in the exact penalty function completes the algorithm description. Global convergence is established, and a comparison with alternative algorithms is made.

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