A New Superlinearly Convergent Strongly Subfeasible Sequential Quadratic Programming Algorithm for Inequality-Constrained Optimization

Abstract

Combining the ideas of generalized projection and the strongly subfeasible sequential quadratic programming (SQP) method, we present a new strongly subfeasible SQP algorithm for nonlinearly inequality-constrained optimization problems. The algorithm, in which a new unified step-length search of Armijo type is introduced, starting from an arbitrary initial point, produces a feasible point after a finite number of iterations and from then on becomes a feasible descent SQP algorithm. At each iteration, only one quadratic program needs to be solved, and two correctional directions are obtained simply by explicit formulas that contain the same inverse matrix. Furthermore, the global and superlinear convergence results are proved under mild assumptions without strict complementarity conditions. Finally, some preliminary numerical results show that the proposed algorithm is stable and promising.

A strongly sub-feasible primal-dual quasi interior-point algorithm for nonlinear inequality constrained optimization

“…In fact, such a difficulty not only appears here but also in many other methods of feasible type, such as feasible sequential quadratic programming [7] and feasible sequential quadratically constrained quadratic programming [8]. In order to overcome such kind of difficulty in a more general context, Jian and his collaborators proposed a method of strongly sub-feasible directions (MSSFD), see [9,Chapter 2] and [10][11][12][13]. The main features of the MSSFD can be described as follows: the initial point can be chosen arbitrarily without using any penalty parameters or penalty functions; the feasibility of a constraint is maintained through the iterations once it is reached, and therefore the number of feasible constraints is nondecreasing; the operations of initialization (Phase I) and optimization (Phase II) can be well unified automatically.…”

An improved sequential quadratic programming algorithm for solving general nonlinear programming problems

“…is the KKT point of problem (3). Moreover, {i ∈ I : λ * i > 0} = {i ∈ I 1 : µ * i > 0} ∪ I 2 , which implies that KKT pair (x * , λ * ) of problem (3) also satisfies the strong second-order sufficiency conditions, i.e.,…”

“…In this paper we consider the following nonlinear programming problem Sequential quadratic programming (SQP) algorithms have been widely studied by many authors during the past several decades, e.g., Refs. [1,2,3,4,5,6,7], and have been proved highly effective for solving problem (1). SQP algorithms generate iteratively the main search directions by solving the standard quadratic programming (QP) subproblem min g 0 (x) T…”

A superlinearly convergent hybrid algorithm for solving nonlinear programming

“…In [13], Jian, et.al., present a new SQP algorithm for solving problem (NIO) by using of subproblem (QP2). The correctional directions are obtained by explicit formulas in which the generalized projection technique is applied.…”

“…In this paper, motivated by the algorithm ideas in [13] and the method of quasistrongly sub-feasible directions in [14], a new algorithm is proposed for solving problem (NIO). The main search direction is obtained by a convex combination of d 0 and a mere feasible direction d 2 which are generated by solving a QP subproblem and a SLE, respectively.…”