Global convergence to rst-order critical points is proved for two trust-region SQP-lter algorithms of the type introduced by Fletcher and Leyyer (1997). The algorithms allow for an approximate solution of the quadratic subproblem and incorporate the safeguarding tests described in Fletcher, Leyyer and Toint (1998). The rst algorithm decomposes the step into its normal and tangential components ...

where u ∈ Ru are independent decision variables subject to the bounds u and u – the curly brackets (≺) denoting componentwise inequality – and φ, g : Ru → R are cost and constraint functions, respectively. The characteristic element of (1.1) is the presence of experimental functions, denoted by the subscript p (for “plant”), which may only be evaluated by conducting an experiment for a given ch...

The Powell singular function was introduced 1962 by M.J.D. Powell as an unconstrained optimization problem. The function is also used as nonlinear least squares problem and system of nonlinear equations. The function is a classic test function included in collections of test problems in optimization as well as an example problem in text books. In the global optimization literature the function ...

Stabilized sequential quadratic programming (SQP) methods for nonlinear optimization are designed to provide a sequence of iterates with fast local convergence regardless of whether or not the active-constraint gradients are linearly dependent. This paper concerns the global convergence properties of a stabilized SQP method with a primal-dual augmented Lagrangian merit function. The proposed me...

In many natural synchronization phenomena, communication between individual elements occurs not directly but rather through the environment. One of these instances is bacterial quorum sensing, where bacteria release signaling molecules in the environment which in turn are sensed and used for population coordination. Extending this motivation to a general nonlinear dynamical system context, this...

In the efficient global optimization problem, we minimize an unknown function f , using as few observations f (x) as possible. It can be considered a continuum-armed-bandit problem, with noiseless data, and simple regret. Expected-improvement algorithms are perhaps the most popular methods for solving the problem; in this paper, we provide theoretical results on their asymptotic behaviour. Impl...

Gould and Robinson (NAR 08/18, Oxford University Computing Laboratory, 2008) gave global convergence results for a second-derivative SQP method for minimizing the exact l1-merit function for a fixed value of the penalty parameter. To establish this result, we used the properties of the so-called Cauchy step, which was itself computed from the so-called predictor step. In addition, we allowed fo...

where the Ai . 0 and 21 , ai , 1 for i 1⁄4 1; . . . ; p. By a logarithmic change of coordinates, equation (2) is converted to a difference equation of type (1), and it can be concluded from Corollary 2.4 that (2) converges to maxA 1=ð12aiÞ i for all positive initial conditions. Max-type difference equations have been considered by a number of authors, including [1–9,11–14]. Ladas poses an inter...

A population of players repeatedly plays an n strategy symmetric game. Players update their strategies by sampling the behavior of k opponents and playing a best response to the distribution of strategies in the sample. Suppose the game possesses a 1 k -dominant strategy which is initially played by a positive fraction of the population. Then if the population size is large enough, play converg...