A recursive quadratic programming algorithm that uses differentiable exact penalty functions
Mathematical Programming: Series A and B
A nonmonotone line search technique for Newton's method
SIAM Journal on Numerical Analysis
Trust region algorithms for optimization with nonlinear equality and inequality constraints
Trust region algorithms for optimization with nonlinear equality and inequality constraints
A trust region algorithm for equality constrained optimization
Mathematical Programming: Series A and B
Nonmonotonic trust region algorithm
Journal of Optimization Theory and Applications
A projective quasi-Newton method for nonlinear optimization
Journal of Computational and Applied Mathematics
Nonmonotonic projected algorithm with both trust region and line search for constrained optimization
Journal of Computational and Applied Mathematics
A Trust Region Interior Point Algorithm for Linearly Constrained Optimization
SIAM Journal on Optimization
Nonmonotonic back-tracking trust region interior point algorithm for linear constrained optimization
Journal of Computational and Applied Mathematics
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
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In this paper, we propose a new nonmonotonic interior point backtracking strategy to modify the reduced projective affine scaling trust region algorithm for solving optimization subject to nonlinear equality and linear inequality constraints. The general full trust region subproblem for solving the nonlinear equality and linear inequality constrained optimization is decomposed to a pair of trust region subproblems in horizontal and vertical subspaces of linearize equality constraints and extended affine scaling equality constraints. The horizontal subproblem in the proposed algorithm is defined by minimizing a quadratic projective reduced Hessian function subject only to an ellipsoidal trust region constraint in a null subspace of the tangential space, while the vertical subproblem is also defined by the least squares subproblem subject only to an ellipsoidal trust region constraint. By introducing the Fletcher's penalty function as the merit function, trust region strategy with interior point backtracking technique will switch to strictly feasible interior point step generated by a component direction of the two trust region subproblems. The global convergence of the proposed algorithm while maintaining fast local convergence rate of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion should bring about speeding up the convergence progress in some high nonlinear function conditioned cases.