Interior Point Approach to Linear, Quadratic and Convex Programming

Duality and a Farkas lemma for integer programs

“…Den Hertog [9]). This should not be a surprise as a self-concordant barrier function φ K (x) of a cone K ⊂ R n is given by the logarithm of Laplace transform K * e − x,s ds of its dual cone K * (see e.g.…”

On the Design of Optimal Measurements for Antenna Near-Field Imaging Problems

“…[20] developed an optimality criterion based on the determinant of the Fisher information matrix, a topic which has been further developed in e.g., [22,25]. The convex Fisher information measure was proposed already in the early 80's [20], but a comprehensive exploitation of the ecient polynomial time interior point methods for convex optimization that has been established during the 90's (including determinant maximization) seem to be missing, see e.g., [7,15,24].…”

“…The purpose of this paper is to provide a mathematical framework for optimization of in- eld [1,6,9], the Fisher information [10] to quantify the quality of data and use of modern interior point convex optimization techniques [7,15,24].…”

Examples of ill-behaved central paths in convex optimization

“…Internal penalty methods, also known as barrier methods, had an explosive development in the last fifteen years, due to the success of interior point methods for linear programming and for linear complementarity problems (see the monographs [10,18,19,25,27,28,33]; see also the extensions to nonlinear programming in [4,9,11,14,15,29]). The first deep study of the path of optimizers, now known as central path, is due to McLinden [21], followed by Bayer and Lagarias [3] and by Megiddo [22], who gave a definitive characterization of the primal-dual central path.…”