Nonlinear Optimization
Cetraro, July 1-7, 2007

Sequential Quadratic Programming

Prof. Roger Fletcher, Univ. of Dundee, UK


1) Fundamentals, the NLP problem, special cases, Newton's method, Unconstrained optimization, Optimization with equality constraints, Linear constraints, Null space methods.

2) Nonlinear constraints, regularity, Inverse function theorem, Local optimality conditions, Lagrange multipliers, Interpretation, Second order conditions.

3) Method of Lagrange multipliers, SEQP method, Inequality constraints, optimality conditions, Quadratic Programming, Active Set Method, SQP method.

4) Globalization of NLP methods, Penalty functions, Historical perspective, Interior Point methods, Augmented Lagrangians, MINOS, SNOPT, L1 penalty function, SL1QP method.

5) Filter methods, domination, feasibility restoration, blocking, convergence theory.

6) Recent developments, Hessian approximations, conjugate gradient methods.

7) Modelling Languages, AMPL, TOMLAB, NEOS, Syntax, Examples illustrating useful constructions.