Interior-point methods have proven to be efficient for the solution of large, sparse linear and quadratic programming problems. We propose to extend these methods to cover more general classes of problems. In particular, we plan to apply interior-point technology to create efficient algorithms for the solution of convex programming problems. Examples of critical decision/design problems that are convex but neither quadratic nor linear include compliance minimization in structural optimization, antenna array synthesis problems, image analysis and deblurring, tomography, $L^1$-regression, constrained facility location problems, finding minimal surfaces, scheduling problems in which costs are not proportional to scale, and robust optimization models.
As diverse as the above convex optimization problems are, many important optimization problems are not convex and therefore must be handled using methods of global optimization. Many of the nonconvex global optimization problems fall into the general problem category of parameter optimization. Other examples include trajectory optimization, problems in modem design (e.g. spacing $n$ points on a unit sphere as far apart as possible), and the design of composite materials with desired properties. We recently showed how to extend the main technique of Lipschitz global optimization to the larger class of continuous (not-necessarily-Lipschitz) functions. We propose to continue this line of research by developing specific algorithms that are applicable to this larger problem domain. These algorithms are amenable to parallelization. We plan to implement not only serial versions of the algorithms but parallel versions as well.