269 research outputs found
Hybrid Newton-type method for a class of semismooth equations
In this paper, we present a hybrid method for the solution of a class of composite semismooth equations encountered frequently in applications. The method is obtained by combining a generalized finite-difference Newton method to an inexpensive direct search method. We prove that, under standard assumptions, the method is globally convergent with a local rate of convergence which is superlinear or quadratic. We report also several numerical results obtained applying the method to suitable reformulations of well-known nonlinear complementarity problem
Projection methods in conic optimization
There exist efficient algorithms to project a point onto the intersection of
a convex cone and an affine subspace. Those conic projections are in turn the
work-horse of a range of algorithms in conic optimization, having a variety of
applications in science, finance and engineering. This chapter reviews some of
these algorithms, emphasizing the so-called regularization algorithms for
linear conic optimization, and applications in polynomial optimization. This is
a presentation of the material of several recent research articles; we aim here
at clarifying the ideas, presenting them in a general framework, and pointing
out important techniques
Preconditioning of Active-Set Newton Methods for PDE-constrained Optimal Control Problems
We address the problem of preconditioning a sequence of saddle point linear
systems arising in the solution of PDE-constrained optimal control problems via
active-set Newton methods, with control and (regularized) state constraints. We
present two new preconditioners based on a full block matrix factorization of
the Schur complement of the Jacobian matrices, where the active-set blocks are
merged into the constraint blocks. We discuss the robustness of the new
preconditioners with respect to the parameters of the continuous and discrete
problems. Numerical experiments on 3D problems are presented, including
comparisons with existing approaches based on preconditioned conjugate
gradients in a nonstandard inner product
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