Internet search engines have become an indispensable part of everyday living and business today. Although the capabilities of Internet search engines are incrementally improving steadily, it may be time for us to explore a few new directions that can take the search engines to the next level. In this article, we will summarize the current activities in advancing the state of Internet search eng...

In this article we consider modiied search directions in the endgame of interior point methods for linear programming. In this stage, the normal equations determining the search directions become ill-conditioned. The modiied search directions are computed by solving perturbed systems in which the systems may be solved ef-ciently by the preconditioned conjugate gradient solver. We prove the conv...

We describe and critique the convergence properties of filterbased evolutionary pattern search algorithms (F-EPSAs). F-EPSAs implicitly use a filter to perform a multi-objective search for constrained problems such that convergence can be guaranteed. We provide two examples that illustrate how F-EPSAs may generate limit points other than constrained stationary points. F-EPSAs are evolutionary p...

The Commutative Class of search directions for semidefinite programming is first proposed by Monteiro and Zhang [13]. In this paper, we investigate the corresponding class of search directions for linear programming over symmetric cones, which is a class of convex optimization problems including linear programming, second-order cone programming, and semidefinite programming as special cases. Co...

Various search directions used in interior-point-algorithms for the SDP (semidefinite program) and the monotone SDLCP (semide nite linear complementarity problem) are characterized by the intersection of a maximal monotone a ne subspace and a maximal and strictly antitone a ne subspace. This observation provides a uni ed geometric view over the existence of those search directions.

We propose a new technique for minimization of convex functions not necessarily smooth. Our approach employs an equivalent constrained optimization problem and approximated linear programs obtained with cutting planes. At each iteration a search direction and a step length are computed. If the step length is considered “non serious”, a cutting plane is added and a new search direction is comput...