Preprint A675/2010
Semismooth SQP method for equality-constrained optimization problems with an application to the lifted reformulation of mathematical programs with complementarity constraints

M.V. Solodov | Izmailov, A.F. | Pogosyan, A.L.

**Keywords: **

We consider the sequential quadratic programming
algorithm (SQP) applied to equality-constrained optimization problems,
where the problem data is differentiable with Lipschitz-continuous
first derivatives. For this
setting, Dennis-Moré type
analysis of primal superlinear convergence is presented.
Our main motivation is a special modification of SQP
tailored to the structure of the lifted reformulation of
mathematical programs with complementarity constraints (MPCC). For this
problem, we propose a special positive definite modification
of the matrices in the generalized Hessian, which is suitable
for globalization of SQP based on the penalty function,
and at the same time can be expected to satisfy our general
Dennis-Moré type conditions, thus preserving local
superlinear convergence. (Standard quasi-Newton updates
in the SQP framework require twice differentiability
of the problem data at the solution
for superlinear convergence.)
Preliminary numerical results
comparing a number of quasi-Newton versions of semismooth
SQP applied to MPCC are also reported.