<Para ID="Par1">Clustering is an important problem in data mining. It can be formulated as a nonsmooth, nonconvex optimization problem. For the most global optimization techniques this problem is challenging even in medium size data sets. In this paper, we propose an approach that allows one to apply local...</para>

<Para ID="Par1">Sometimes, the feasible set of an optimization problem that one aims to solve using a Nonlinear Programming algorithm is empty. In this case, two characteristics of the algorithm are desirable. On the one hand, the algorithm should converge to a minimizer of some infeasibility measure. On the...</para>

The NP-hard nature of cardinality constrained mean-variance portfolio optimization problems has led to a number of different algorithms with varying degrees of success in reaching optimality given limited computational resources and under the presence of strict time constraints present in...

The Constraint Consensus method moves quickly from an initial infeasible point to a point that is close to feasibility for a set of nonlinear constraints. It is a useful first step prior to launching an expensive local solver, improving the probability that the local solver will find a solution...

A trust-region-based derivative free algorithm for solving bound constrained mixed integer nonlinear programs is developed in this paper. The algorithm is proven to converge to a local minimum after a finite number of function evaluations. In addition, an improved definition of local minima of...

<Para ID="Par1">Sequential quadratic programming (SQP) methods are known to be efficient for solving a series of related nonlinear optimization problems because of desirable hot and warm start properties—a solution for one problem is a good estimate of the solution of the next. However, standard SQP solvers...</para>

The paper proposes a primal-dual algorithm for solving an equality constrained minimization problem. The algorithm is a Newton-like method applied to a sequence of perturbed optimality systems that follow naturally from the quadratic penalty approach. This work is first motivated by the fact...

A globally convergent algorithm based on the stabilized sequential quadratic programming (sSQP) method is presented in order to solve optimization problems with equality constraints and bounds. This formulation has attractive features in the sense that constraint qualifications are not needed at...

In this paper, we present a primal-dual interior-point method for solving nonlinear programming problems. It employs a Levenberg-Marquardt (LM) perturbation to the Karush-Kuhn-Tucker (KKT) matrix to handle indefinite Hessians and a line search to obtain sufficient descent at each iteration. We...