On the convergence of a sequential quadratic programming method with an augmented lagrangian line search function

On the Asymptotic Superlinear Convergence of the Augmented Lagrangian Method for Semidefinite Programming with Multiple Solutions

Solving large scale convex semidefinite programming (SDP) problems has long been a challenging task numerically. Fortunately, several powerful solvers including SDPNAL, SDPNAL+ and QSDPNAL have recently been developed to solve linear and convex quadratic SDP problems to high accuracy successfully. These solvers are based on the augmented Lagrangian method (ALM) applied to the dual problems with...

On the local quadratic convergence of the primal-dual augmented Lagrangian method

We consider a Primal-Dual Augmented Lagrangian (PDAL) method for optimization problems with equality constraints. Each step of the PDAL requires solving the Primal-Dual linear system of equations. We show that under the standard second-order optimality condition the PDAL method generates a sequence, which locally converges to the primal-dual solution with quadratic rate.

The Sequential Quadratic Programming Method

Sequential (or Successive) Quadratic Programming (SQP) is a technique for the solution of Nonlinear Programming (NLP) problems. It is, as we shall see, an idealized concept, permitting and indeed necessitating many variations and modifications before becoming available as part of a reliable and efficient production computer code. In this monograph we trace the evolution of the SQP method throug...

A TRUST-REGION SEQUENTIAL QUADRATIC PROGRAMMING WITH NEW SIMPLE FILTER AS AN EFFICIENT AND ROBUST FIRST-ORDER RELIABILITY METHOD

The real-world applications addressing the nonlinear functions of multiple variables could be implicitly assessed through structural reliability analysis. This study establishes an efficient algorithm for resolving highly nonlinear structural reliability problems. To this end, first a numerical nonlinear optimization algorithm with a new simple filter is defined to locate and estimate the most ...

A Quadratic Approximation Method Based on Augmented Lagrangian Functions for Nonconvex Nonlinear Programming Problems