A very simple SQCQP method for a class of smooth convex constrained minimization problems with nice convergence results

作者：Auslender Alfred^*

来源：Mathematical Programming, 2013, 142(1-2): 349-369.

DOI：10.1007/s10107-012-0582-3

• Smooth convex constrained minimization
• Quadratically constrained quadratic programming
• Sequential quadratic programming
• Convergence rate
• Optimal projected gradient schemes

We introduce a new and very simple algorithm for a class of smooth convex constrained minimization problems which is an iterative scheme related to sequential quadratically constrained quadratic programming methods, called sequential simple quadratic method (SSQM). The computational simplicity of SSQM, which uses first-order information, makes it suitable for large scale problems. Theoretical results under standard assumptions are given proving that the whole sequence built by the algorithm converges to a solution and becomes feasible after a finite number of iterations. When in addition the objective function is strongly convex then asymptotic linear rate of convergence is established.

• 出版日期2013-12