The problem of finding singularities of monotone vectors fields on Hadamard manifolds will be considered and solved by extending the well-known proximal point algorithm. For monotone vector fields the algorithm will generate a well defined sequence, and for monotone vector fields with singularities it will converge to a singularity. It will be also shown how … Read more
A hybrid interior-point method for nonlinear programming is presented. It enjoys the flexibility of switching between a line search based method which computes steps by factoring the primal-dual equations and an iterative method using a conjugate gradient algorithm and globalized by means of trust regions. Steps computed by a direct factorization are always tried first, … Read more
We find very often in the industry simulators of huge chemical reactors, simulators of huge turbo-compressors, simulators of the path of a satellite in low orbit around earth, … These simulators were written to allow the design engineer to correctly estimate the consequences of the adjustment of one (or many) design variables (or parameters of … Read more
We consider the variational inequality problem formed by a general set-valued maximal monotone operator and a possibly unbounded “box” in $R^n$, and study its solution by proximal methods whose distance regularizations are coercive over the box. We prove convergence for a class of double regularizations generalizing a previously-proposed class of Auslender et al. We apply … Read more
This paper is about an intriguing property of the continuous Newton-Raphson method for the minimization of a continuous objective function f: if x is a point in the domain of attraction of a strict local minimizer x* then the flux line of the Newton-Raphson flow that starts in x approaches x* from a direction that … Read more
This paper uses certain conditions for the global and superlinear convergence of the two-parameter self-scaling Broyden family of quasi-Newton algorithms for unconstraiend optimization to derive a wide interval for self-scaling updates. Numerical testing shows that such algorithms not only accelerate the convergence of the (unscaled) methods from the so-called convex class, but increase their chances … Read more
An optimal control solution to a fed-batch fermentation process, responding to a competition call, was developed using NEOS Server. Substantial improvement to the nominal performance achieved in the paper demonstrates the ability of the NEOS Server and the APPS algorithm. Citation Proceedings of Inst. of Mechanical Engineers , Part-I (UK). To appear. (Accepted May 2003). … Read more
Gradient projection methods based on the Barzilai-Borwein spectral steplength choices are considered for quadratic programming problems with simple constraints. Well known nonmonotone spectral projected gradient methods and variable projection methods are discussed. For both approaches the behavior of different combinations of the two spectral steplengths is investigated. A nw adaptive stplength alternating rule is proposed, … Read more
A refined version of the Karush-John first order optimality conditions is presented which reduces the number of constraints for which a constraint qualification is needed. This version is a generalization both of the Karush-John conditions and of the first order optimality conditions for concave constraints. Article Download View Sharpening the Karush-John optimality conditions
We present a modification of Dykstra’s algorithm which allows us to avoid projections onto general convex sets. Instead, we calculate projections onto either a halfspace or onto the intersection of two halfspaces. Convergence of the algorithm is established and special choices of the halfspaces are proposed. The option to project onto halfspaces instead of general … Read more