Using standard nonlinear programming (NLP) theory, we establish formulas for first and second order directional derivatives for optimal value functions of parametric mathematical programs with complementarity constraints (MPCCs). The main point is that under a linear independence condition on the active constraint gradients, optimal value sensitivity of MPCCs is essentially the same as for NLPs...

In the context of a variation of the standard UFL (Uncapacitated Facility Location) problem, but with an objective function that is a separable convex quadratic function of the transportation costs, we present some techniques for improving relaxations of MINLP formulations. We use a disaggregation principal and a strategy of developing model-specific valid inequalities (some nonlinear), which e...

We present an approach for nonlinear programming (NLP) based on the direct minimization of an exact differentiable penalty function using trust-region Newton techniques. As opposed to existing algorithmic approaches to NLP, the approach provides all the features required for scalability: it can efficiently detect and exploit directions of negative curvature, it is superlinearly convergent, and ...

The design of telecommunication network with capacity constraints of links, routers and ports of routers is considered in this paper. Specially, we limit each demand flow traversed through a pre-specified maximal number of links (called hops) under node failure scenarios in IP layer network. Such a design must be the most cost-effective and ensure that feasible flows continue to exist even when...

Reverse convex programming (RCP) represents an important class of global optimization problems consisting of concave cost and inequality constraint functions. While useful in many practical scenarios due to the frequent appearance of concave models, a more powerful, though somewhat abstractly recognized, characteristic of the RCP problem is its ability to approximate a very general class of non...

T algorithm described here, called OptQuest/NLP or OQNLP, is a heuristic designed to find global optima for pure and mixed integer nonlinear problems with many constraints and variables, where all problem functions are differentiable with respect to the continuous variables. It uses OptQuest, a commercial implementation of scatter search developed by OptTek Systems, Inc., to provide starting po...

Finding good (or even just feasible) solutions for Mixed-Integer Nonlinear Programming problems independently of the specific problem structure is a very hard but practically important task, especially when the objective and/or the constraints are nonconvex. With this goal in mind, we present a general-purpose heuristic based on Variable Neighborhood Search, Local Branching, a local Nonlinear P...

In this paper we describe an Interior Point Method (IPM) to solve large scale NonLinear Programming (NLP) problems, tailored to the solution of a specialized Optimal Power Plow (OPF) formulation that uses bus voltages in rectangular coordinates. The distinctive feature of this OPF formulation is that the objective function and constraints are quadratic functions, and such quadratic properties a...

In this paper, we propose nonlinear programming formulations (NLP) and DC (Difference of Convex functions) programming approaches for the asymmetric eigenvalue complementarity problem (EiCP). The EiCP has a solution if and only if these NLPs have zero global optimal value. We reformulate the NLPs as DC Programs (DCP) which can be efficiently solved by DCA (DC Algorithm). Some preliminary numeri...