A simple feasible SQP algorithm for inequality constrained optimization
The author considers a constrained nonlinear minimization problem of the form \[ \text{minimize }f(x)\text{ subject to }g_j(x)\leq 0,\quad j= 1,\dots, m,\tag{\(*\)} \] where \(f: \mathbb{R}^n\to \mathbb{R}^1\), \(g_j: \mathbb{R}^n\to \mathbb{R}^1\) for \(j= 1,\dots, m\) are smooth functions. A new modification of the sequential quadratic programming (SQP) algorithm for solving this problem is proposed. The search direction is a suitable combination of a descent direction, a feasible direction, and a second-order direction. The proposed algorithm either stops at the Karush-Kuhn-Tucker point of problem \((*)\), or generates an infinite sequence \(\{x^k\}\), any accumulation point of which is a Karush-Kuhn-Tucker point of problem \((*)\). Global as well as superlinear convergence under suitable additional conditions is proved.
sequential quadratic programming methods
scientific article; zbMATH DE number 5115370
scientific article