The Crawling Phenomenon in Sequential Convex Programming

Abstract

The paper examines the so-called crawling phenomenon for a class of sequential convex programming algorithms. These algorithms are designed to solve non-convex optimization problems by using convex approximations, trust regions and relaxations. The crawling phenomenon occurs when the iterates of the algorithm get as close as permitted to each other, yet these iterates are not close to a stationary point of the original non-convex problem. It is shown that once the design parameters for a general class of such iterative algorithms are fixed, there are generic problem instances that lead to the crawling phenomenon. A simple example and potential remedies to address this phenomenon are also presented.