Evaluation complexity for convexly constrained optimization is considered and it is shown first that the complexity bound of O(ǫ) proved by Cartis, Gould and Toint (IMAJNA 32(4) 2012, pp.1662-1695) for computing an ǫ-approximate first-order critical point can be obtained under significantly weaker assumptions. Moreover, the result is generalized to the case where high-order derivatives are used...

We present two bilevel programming formulations for the aircraft deconfliction problem: one based on speed regulation in k dimensions, other heading angle changes 2 dimensions. propose three reformulations of each problem KKT conditions and different duals lower-level subproblems. also a cut generation algorithm to solve formulations. Finally, we computational results variety instances.

Regularized and stabilized sequential quadratic programming methods are two classes of sequential quadratic programming (SQP) methods designed to resolve the numerical and theoretical difficulties associated with ill-posed or degenerate nonlinear optimization problems. Recently, a regularized SQP method has been proposed that provides a strong connection between augmented Lagrangian methods and...

The lecture presents an integrated modeling and solution framework aiming at the robust and efficient solution of very large instances of tree-sparse programs. This wide class of nonlinear programs (NLP) is characterized by an underlying tree topology. It includes, in particular, dynamic stochastic programs in scenario tree formulation, multistage stochastic programs, where the objective and co...

Mathematical programs with equilibrium (or complementarity) constraints (MPECs for short) form a difficult class of optimization problems. The standard KKT conditions are not always necessary optimality conditions due to the fact that suitable constraint qualifications are often violated. Alternatively, one can therefore use the Fritz John-approach to derive necessary optimality conditions. Whi...

For a long time, the bilevel programming problem has essentially been considered as a special case of mathematical programs with equilibrium constraints (MPECs), in particular when the so-called KKT reformulation is in question. Recently though, this widespread believe was shown to be false in general. In this paper, other aspects of the difference between both problems are revealed as we consi...

1. Abstract The hybrid cellular automaton (HCA) method is a biologically inspired algorithm capable of topology synthesis that was developed to simulate the behavior of the bone functional adaptation process. In this algorithm, the design domain is divided into cells with some communication property among neighbors. Local evolutionary rules, obtained from classical control theory, iteratively e...

We describe a general scheme for solving nonconvex optimization problems, where in each iteration the nonconvex feasible set is approximated by an inner convex approximation. The latter is defined using an upper bound on the nonconvex constraint functions. Under appropriate conditions on this upper bounding convex function, a monotone convergence to a KKT point is established. The scheme is app...