Based on extensive computational evidence (hundreds of thousands of randomly generated problems) the second author conjectured that $\bar{\kappa}(\zeta)=1$, which is a factor of $\sqrt{2n}$ better than that has been proved, and which would yield an $O(\sqrt{n})$ iteration full-Newton step infeasible interior-point algorithm. In this paper we present an example showing that $\bar{\kappa}(\zeta)$ is in the … Read more
This paper proposes an infeasible interior-point algorithm with full-Newton step for linear programming, which is an extension of the work of Roos (SIAM J. Optim., 16(4):1110–1136, 2006). We introduce a kernel function in the algorithm. For $p\in[0,1)$, the polynomial complexity can be proved and the result coincides with the best result for infeasible interior-point methods, … Read more
In this paper we study linear optimization problems with multi-dimensional linear positive second-order stochastic dominance constraints. By using the polyhedral properties of the second- order linear dominance condition we present a cutting-surface algorithm, and show its finite convergence. The cut generation problem is a difference of convex functions (DC) optimization problem. We exploit the polyhedral … Read more
Given a connected graph $G=(N,E)$ with node weights $s\in\R^N_+$ and nonnegative edge lengths, we study the following embedding problem related to an eigenvalue optimization problem over the second smallest eigenvalue of the (scaled) Laplacian of $G$: Find $v_i\in\R^{|N|}$, $i\in N$ so that distances between adjacent nodes do not exceed prescribed edge lengths, the weighted barycenter … Read more
Option price data is often used to infer risk-neutral densities for future prices of an underlying asset. Given the prices of a set of options on the same underlying asset with different strikes and maturities, we propose a nonparametric approach for estimating the evolution of the risk-neutral density in time. Our method uses bicubic splines … Read more
This paper proposes a primal-dual interior-point filter method for nonlinear semidefinite programming, which is the first multidimensional (three-dimensional) filter methods for interior-point methods, and of course for constrained optimization. A freshly new definition of filter entries is proposed, which is greatly different from those in all the current filter methods. A mixed norm is used … Read more
Semidefinite Programming (SDP) may be seen as a generalization of Linear Programming (LP). In particular, one may extend interior point algorithms for LP to SDP, but it has proven much more difficult to exploit structure in the SDP data during computation. We survey three types of special structure in SDP data: 1) a common `chordal’ … Read more
This work addresses the computation of free-energy di fferences between protein conformations by using morphing (i.e., transformation) of a source conformation into a target conformation. To enhance the morph- ing procedure, we employ permutations of atoms; we transform atom n in the source conformation into atom \sigma(n) in the target conformation rather than directly transforming atom … Read more
Lecture notes for the tutorial at the workshop HPOPT 2008 – 10th International Workshop on High Performance Optimization Techniques (Algebraic Structure in Semidefinite Programming), June 11th to 13th, 2008, Tilburg University, The Netherlands. CitationarXiv:0809.2017v1 [math.OC]ArticleDownload View PDF
In this paper, we study a gradient based method for general cone programming (CP) problems. In particular, we first consider four natural primal-dual convex smooth minimization reformulations for them, and then discuss a variant of Nesterov’s smooth (VNS) method recently proposed by Tseng [30] for solving these reformulations. The associated worst-case major arithmetic operations costs … Read more