2 Semidefinite Programming: Duality, Algorithms, Complexity, and Geometry 3 2.1 Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Geometry . . ...

We present a new approach to the design of D-optimal experiments with multivariate polynomial regressions on compact semi-algebraic design spaces. We apply the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically and approximately the optimal design problem. The geometry of the design is recovered with semidefinite programming duality theory and the Christof...

In this report, some results on semidefinite programming relaxation of graph coloring are summarized. Two algorithms on semicoloring/coloring are described in detail for 3-colorable graphs. The relation between semidefinite programming relaxation and the Lovász theta function is simply introduced.

In this short note a sensitivity result for quadratic semidefinite programming is presented under a weak form of second order sufficient condition. Based on this result, also the local convergence of a sequential quadratic semidefinite programming algorithm extends to this weak second order sufficient condition. Mathematical subject classification: 90C22, 90C30, 90C31, 90C55.

1 Overview We survey the basic notions of cones and cone-LP and give several examples mostly related to semidefinite programming. The linear and semidefinite programming problems are formulated as follows: Let c ∈ n and b ∈ m ,A ∈ n×m with rows a i ∈

Copositive programming is a relative young field which has evolved into a highly active research area in mathematical optimization. An important line of research is to use semidefinite programming to approximate conic programming over the copositive cone. Two major drawbacks of this approach are the rapid growth in size of the resulting semidefinite programs, and the lack of information about t...

We describe an implementation of nonsymmetric interior-point methods for linear cone programs defined by two types of matrix cones: the cone of positive semidefinite matrices with a given chordal sparsity pattern and its dual cone, the cone of chordal sparse matrices that have a positive semidefinite completion. The implementation takes advantage of fast recursive algorithms for evaluating the ...

The convergence of primal and dual central paths associated to entropy and exponential functions, respectively, for semidefinite programming problem are studied in this paper. As an application, the proximal point method with the Kullback-Leibler distance applied to semidefinite programming problems is considered, and the convergence of primal and dual sequences is proved.

In this paper we consider covariance structural models with which we associate semidefinite programming problems. We discuss statistical properties of estimates of the respective optimal value and optimal solutions when the ‘true’ covariance matrix is estimated by its sample counterpart. The analysis is based on perturbation theory of semidefinite programming. As an example we discuss asymptoti...