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
One of the most efficient interior-point methods for some classes of primal block-angular problems solves the normal equations by a combination of Cholesky factorizations and preconditioned conjugate gradient for, respectively, the block and linking constraints. Its efficiency depends on the spectral radius—in [0,1)—of a certain matrix in the definition of the preconditioner. Spectral radius close … Read more
We propose the DISCO algorithm for graph realization in $\real^d$, given sparse and noisy short-range inter-vertex distances as inputs. Our divide-and-conquer algorithm works as follows. When a group has a sufficiently small number of vertices, the basis step is to form a graph realization by solving a semidefinite program. The recursive step is to break … Read more
Solvers for semidefinite programming (SDP) have evolved a great deal in the last decade, and their development continues. In order to further support and encourage this development, we present a new test set of SDP instances. These instances arise from recent applications of SDP in coding theory, computational geometry, graph theory and structural design. Most … Read more
In this paper we derive new upper bounds for the densities of measurable sets in R^n which avoid a finite set of prescribed distances. The new bounds come from the solution of a linear programming problem. We apply this method to obtain new upper bounds for measurable sets which avoid the unit distance in dimensions … Read more
We observe that in a simple one-dimensional polynomial optimization problem (POP), the `optimal’ values of semidefinite programming (SDP) relaxation problems reported by the standard SDP solvers converge to the optimal value of the POP, while the true optimal values of SDP relaxation problems are strictly and significantly less than that value. Some pieces of circumstantial … Read more
The elegant results for strong duality and strict complementarity for linear programming, \LP, can fail for cone programming over nonpolyhedral cones. One can have: unattained optimal values; nonzero duality gaps; and no primal-dual optimal pair that satisfies strict complementarity. This failure is tied to the nonclosure of sums of nonpolyhedral closed cones. We take a … Read more
In this paper we present an infeasible interior-point algorithm for solving linear optimization problems. This algorithm is obtained by modifying the search direction in the algorithm [C. Roos, A full-Newton step ${O}(n)$ infeasible interior-point algorithm for linear optimization, 16(4) 2006, 1110-1136.]. The analysis of our algorithm is much simpler than that of the Roos’s algorithm … Read more