Abstract
Chapter 3 proposed the coordinate search (CS) algorithm for unconstrained optimization. The algorithm worked based on local exploration around the incumbent solution in the positive and negative orthogonal coordinate directions. In Chapter 7, this algorithm was expanded to allow a broader use of search directions, resulting in the generalised pattern search (GPS) algorithm. However, the convergence analysis of the GPS algorithm falls a little short of what we would like. First, the main result states that if the objective function f is locally Lipschitz, then the generalised directional derivatives are nonnegative for only a finite set of directions. Second, and more importantly, the analysis only examined unconstrained optimization problems. In practice, there are very few problems in which the variables are free to take any values.
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