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Interestingly, theory and algorithms for linear optimization an interior point approach that you really wait for now is coming. It's significant to wait for the representative and beneficial books to read. Every book that is provided in better way and utterance will be expected by many peoples. Even you are a good reader or not, feeling to read this book(More)
Conic quadratic optimization is the problem of minimizing a linear function subject to the intersection of an affine set and the product of quadratic cones. The problem is a convex optimization problem and has numerous applications in engineering, economics, and other areas of science. Indeed, linear and convex quadratic optimization is a special case.(More)
We demonstrate that if A1, ..., Am are symmetric positive semidefinite n×n matrices with positive definite sum and A is an arbitrary symmetric n×n matrix, then the relative accuracy, in terms of the optimal value, of the semidefinite relaxation max X {Tr(AX) | Tr(AiX) ≤ 1, i = 1, ...,m; X 0} (SDP) of the optimization program xTAx→ max | xAix ≤ 1, i = 1,(More)
Abstract. We consider a conic-quadratic (and in particular a quadratically constrained) optimization problem with uncertain data, known only to reside in some uncertainty set U . The robust counterpart of such a problem leads usually to an NP-hard semidefinite problem; this is the case, for example, when U is given as the intersection of ellipsoids or as an(More)
Recently, so-called self-regular barrier functions for primal-dual interior-point methods (IPMs) for linear optimization were introduced. Each such barrier function is determined by its (univariate) self-regular kernel function. We introduce a new class of kernel functions. The class is defined by some simple conditions on the kernel function and its(More)
We present a full-Newton step infeasible interior-point algorithm. It is shown that at most O(n) (inner) iterations suffice to reduce the duality gap and the residuals by the factor 1 e . The bound coincides with the best known bound for infeasible interior-point algorithms. It is conjectured that further investigation will improve the above bound to O( √(More)
A selection of these reports is available in PostScript form at the Faculty's anonymous ftp-Abstract In this paper we propose a method for linear programming with the property that, starting from an initial non{central point, it generates iterates that simultaneously get closer to optimality and closer to centrality. The iterates follow so{called targets,(More)