A globally convergent primal-dual interior-point filter method for nonlinear programming

In this paper, the filter technique of Fletcher and Leyffer (1997) is used to globalize the primal-dual interior-point algorithm for nonlinear programming, avoiding the use of merit functions and the updating of penalty parameters. The new algorithm decomposes the primal-dual step obtained from the perturbed first-order necessary conditions into a normal and a tangential step, whose sizes are controlled by a trust-region type parameter. Each entry in the filter is a pair of coordinates: one resulting from feasibility and centrality, and associated with the normal step; the other resulting from optimality (complementarity and duality), and related with the tangential step. Global convergence to first-order critical points is proved for the new primal-dual interior-point filter algorithm

Income Differentials on Regional Labour Markets in Southwest Germany

The aim of our paper is to identify explanatory variables for income disparities between women and men across different regional types. Using data from the BA Employment Panel (BEP) descriptive statistics show that the gender pay gap grows wider from core regions to periphery. The main explanatory variables for the income differentials are vocational education in the mens case and size of enterprise in the womens case. Whereas in the case of women the importance of vocational status increases and the importance of size of enterprise decreases from rural areas to urban areas.Regional economics, Regional data, Wage differentials, Wage gap

Differentiability results and sensitivity calculation for optimal control of incompressible two-phase Navier-Stokes equations with surface tension

We analyze optimal control problems for two-phase Navier-Stokes equations with surface tension. Based on $L_p$-maximal regularity of the underlying linear problem and recent well-posedness results of the problem for sufficiently small data we show the differentiability of the solution with respect to initial and distributed controls for appropriate spaces resulting form the $L_p$-maximal regularity setting. We consider first a formulation where the interface is transformed to a hyperplane. Then we deduce differentiability results for the solution in the physical coordinates. Finally, we state an equivalent Volume-of-Fluid type formulation and use the obtained differentiability results to derive rigorosly the corresponding sensitivity equations of the Volume-of-Fluid type formulation. For objective functionals involving the velocity field or the discontinuous pressure or phase indciator field we derive differentiability results with respect to controls and state formulas for the derivative. The results of the paper form an analytical foundation for stating optimality conditions, justifying the application of derivative based optimization methods and for studying the convergence of discrete sensitivity schemes based on Volume-of-Fluid discretizations for optimal control of two-phase Navier-Stokes equations

Approximation algorithms for stochastic and risk-averse optimization

We present improved approximation algorithms in stochastic optimization. We prove that the multi-stage stochastic versions of covering integer programs (such as set cover and vertex cover) admit essentially the same approximation algorithms as their standard (non-stochastic) counterparts; this improves upon work of Swamy \& Shmoys which shows an approximability that depends multiplicatively on the number of stages. We also present approximation algorithms for facility location and some of its variants in the $2$-stage recourse model, improving on previous approximation guarantees. We give a $2.2975$-approximation algorithm in the standard polynomial-scenario model and an algorithm with an expected per-scenario $2.4957$-approximation guarantee, which is applicable to the more general black-box distribution model.Comment: Extension of a SODA'07 paper. To appear in SIAM J. Discrete Mat

Operator preconditioning for a class of constrained optimal control problems

We propose and analyze two strategies for preconditioning linear operator equations that arise in PDE constrained optimal control in the framework of conjugate gradient methods. Our particular focus is on control or state constrained problems, where we consider the question of robustness with respect to critical parameters. We construct a preconditioner that yields favorable robustness properties with respect to critical parameters

Operator preconditioning for a class of inequality constrained optimal control problems

Abstract We propose and analyze two strategies for preconditioning linear operator equations that arise in PDE constrained optimal control in the framework of conjugate gradient methods. Our particular focus is on control or state constrained problems, where we consider the question of robustness with respect to critical parameters. We construct a preconditioner that yields favorable robustness properties with respect to critical parameters

Rapid learning of humanoid body schemas with kinematic Bezier maps

Trabajo presentado al 9th IEEE-RAS celebrado en París del 7 al 10 de diciembre de 2009.This paper addresses the problem of hand-eye coordination and, more specifically, tool-eye recalibration of humanoid robots. Inspired by results from neuroscience, a novel method to learn the forward kinematics model as part of the body schema of humanoid robots is presented. By making extensive use of techniques borrowed from the field of computer-aided geometry, the proposed Kinematic Be ́zier Maps (KB-Maps) permit reducing this complex problem to a linearly-solvable, although high-dimensional, one. Therefore, in the absence of noise, an exact kinematic model is obtained. This leads to rapid learning which, unlike in other approaches, is combined with good extrapolation capabilities. These promising theoretical advantages have been validated through simulation, and the applicability of the method to real hardware has been demonstrated through experiments on the humanoid robot ARMAR-IIIa.This work was supported by projects: 'Perception, action & cognition through learning of object-action complexes.' (4915), 'Analysis and motion planning of complex robotic systems' (4802), 'Grup de recerca consolidat - Grup de Robòtica' (4810). The work described in this paper was partially conducted within the EU Cognitive Systems projects GRASP (FP7-215821) and PACO-PLUS (FP6-027657) funded by the European Commission. The authors acknowledge support from the Generalitat de Catalunya under the consolidated Robotics group, and from the Spanish Ministry of Science and Education, under the project DPI2007-60858Peer Reviewe