The first part of this talk is an introduction to sequential quadratic programming (SQP) methods. Specifically, I will i) describe the basic formulation of SQP methods; ii) discuss why SQP methods form a class of very efficient algorithms for solving nonlinear nonconvex optimization problems; and iii) address the main algorithmic difficulties that arise when constructing SQP methods that utilize exact second-derivative information.
The second part of the talk will be focus on recent advances in second-derivative SQP methods. Most of the time will be devoted to describing S2QP: a Fortran 90 implementation of an SQP algorithm that is globally and superlinearly convergent, incorporates second-derivative information efficiently, and utilizes subproblems that are either convex (may be solved efficiently) or need not be solved globally; S2QP may be viewed as an improvement to the Sl1QP method by Fletcher since he requires the global minimizer of indefinite QP subproblems to prove global convergence, which is known to be NP-hard. I will also present limited numerical results from the CUTEr test set, which indicate that S2QP is at least capable of solving (efficiently) some large problems consisting of 10,000-100,000 variables/constraints.
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