(i) The sequence ({H_{k}}) is bounded and satisfies the positive definite restriction (27) with constant (a=underline{varepsilon}), so H2 holds.
The sequence ({H_{k}}) is bounded and satisfies the positive definite restriction (27) with constant (a=underline{varepsilon}), so H2 holds.
(d) Under suitable CQ and assumptions including a relaxed positive definite restriction on the Lagrangian Hessian estimate (H_{k}), but without the isolatedness of the stationary points, the proposed algorithm is globally and superlinearly convergent.
Under suitable CQ and assumptions including a relaxed positive definite restriction on the Lagrangian Hessian estimate (H_{k}), but without the isolatedness of the stationary points, the proposed algorithm is globally and superlinearly convergent.
One is that a new and simple rule to update the penalty parameter ρ in (P ρ ) is derived, the other is that, same as in [18], the uniformly positive definite restriction on the Lagrangian Hessian estimate is relaxed.
The algorithm can start from a feasible point at the boundary of the feasible set, and it possesses global convergence without both the additional assumption of isolatedness of the stationary points and the positive definite restriction on matrix (H_{k}).
(e) A slightly new computation technique for (H_{k}) based on second order derivative information is introduced, which is a modification of the one in [1], Section 5.1, and satisfies the relaxed positive definite restriction. .
A slightly new computation technique for (H_{k}) based on second order derivative information is introduced, which is a modification of the one in [1], Section 5.1, and satisfies the relaxed positive definite restriction.
Waterways are subject to definite geographic and physical restrictions that influence the engineering problems of construction, maintenance, and operation.
