This paper considers the solution of Mixed Integer Nonlinear Programming (MINLP) problems. Classical methods for the solution of MINLP problems decompose the problem by separating the nonlinear part from the integer part. This approach is largely due to the existence of packaged software for solving Nonlinear Programming (NLP) and Mixed Integer Linear Programming problems. In contrast, an integrated approach to solving MINLP problems is considered here. This new algorithm is based on branch-and-bound, but does not require the NLP problem at each node to be solved to optimality. Instead, branching is allowed after each iteration of the NLP solver. In this way, the nonlinear part of the MINLP problem is solved whilst searching the tree. The nonlinear solver that is considered in this paper is a Sequential Quadratic Programming solver. A numerical comparison of the new method with nonlinear branch-and-bound is presented and a factor of about 3 improvement over branch-and-bound is observed...

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We consider minimizing a nonsmooth objective subject to nonsmooth constraints. The nonsmooth functions are approximated by a bundle of subgradients. The novel idea of a lter is used to promote global convergence. Keywords: Nonsmooth optimization, bundle method, lter method. 1 Introduction This paper is concerned with nonsmooth optimization problems where a nonsmooth objective is minimized subject to a nonsmooth constraint. This type of problem can be stated as (P ) 8 < : minimize x f(x) subject to c(x) 0 x 2 X: Throughout the paper, the following assumptions are made: A1 X IR is a bounded polyhedral set. A2 f; c are convex, possibly nonsmooth, locally Lipschitz continuous functions from IR n to IR. A3 For every x (k) 2 X we can evaluate f (k) = f(x (k) ), c (k) = c(x (k) ) and one arbitrary element of their respective generalized gradients g (k) 2 @f (k) = @f(x (k) ) and a (k) 2 @c (k) = @c(x (k) ), where the generalized gradient (or subdieren...

bundle filter method for nonsmooth nonlinear