Interior Point Methods for Semidefinite Programming.

TL;DR: A class of polynomial-time primal–dual interior-point methods for semi-definite optimization based on a new class of kernel functions that are not exponentially convex and also not strongly convex like many usual barrier functions is presented.

TL;DR: An analysis of the full-Newton step infeasible interior-point algorithm for semidefinite optimization, which is an extension of the algorithm introduced by Roos, where I is an identity matrix and V is a symmetric positive definite matrix.

TL;DR: A design algorithm is presented for finding optimal topologies and alignment profiles of additively manufactured, fiber-reinforced composite structures, showing the design is sensitive to both local fiber control and global print angle selection.

TL;DR: The algorithm is a modification of one with no constraint reduction due to Potra and Sheng (1998) and can be applied whenever the data matrices are block diagonal and solves as special cases any optimization problem that is a linear, convex quadratic, conveX quadratically constrained, or second-order cone problem.

TL;DR: It is proved that given a polytopeP and a strictly interior point a εP, there is a projective transformation of the space that mapsP, a toP′, a′ having the following property: the ratio of the radius of the smallest sphere with center a′, containingP′ to theradius of the largest sphere withCenter a′ contained inP′ isO(n).

TL;DR: A survey of the theory and applications of semidefinite programs and an introduction to primaldual interior-point methods for their solution are given.

TL;DR: It is argued that many known interior point methods for linear programs can be transformed in a mechanical way to algorithms for SDP with proofs of convergence and polynomial time complexity carrying over in a similar fashion.

TL;DR: Conditions and an accurate semidefinite programming solver are described in The Journal of the SDPA family for solving large-scale SDPs and in Handbook on Semidefinitely Programming.