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High-dimensional nonlinear optimization problems subject to nonlinearconstraints can appear in several contexts including constrained physical anddynamical systems, statistical estimation, and other numerical models. Feasibleoptimization routines can sometimes be valuable if the objective function isonly defined on the feasible set or if numerical difficulties associated withmerit functions or infeasible termination arise during the use of infeasibleoptimization routines. Drawing on the Riemannian optimization and sequentialquadratic programming literature, a practical algorithm is constructed toconduct feasible optimization on arbitrary implicitly defined constraintmanifolds. Specifically, with $n$ (potentially bound-constrained) variables and$m < n$ nonlinear constraints, each outer optimization loop iteration involvesa single $O(nm^2)$-flop factorization, and computationally efficientretractions are constructed that involve $O(nm)$-flop inner loop iterations. Apackage, LFPSQP.jl, is created using the Julia language that takes advantage ofautomatic differentiation and projected conjugate gradient methods for use ininexact/truncated Newton steps.

Locally Feasibly Projected Sequential Quadratic Programming for Nonlinear Programming on Arbitrary Smooth Constraint Manifolds