This paper studies disjunctive cutting planes in Mixed-Integer Conic Programming. Building on conic duality, we formulate a cut-generating program for separating cuts, and investigate the impact of normalization condition its resolution. In particular, show that careful selection guarantees solvability strong duality. Then, highlight shortcomings conic-infeasible points an outer-approximation c...

We propose a pivotal method for estimating high-dimensional sparse linear regression models, where the overall number of regressors p is large, possibly much larger than n, but only s regressors are significant. The method is a modification of the lasso, called the square-root lasso. The method is pivotal in that it neither relies on the knowledge of the standard deviation σ or nor does it need...

In this paper, a particular shape preserving parametric polynomial approximation of conic sections is studied. The approach is based upon a general strategy to the parametric approximation of implicitly defined planar curves. Polynomial approximants derived are given in a closed form and provide the highest possible approximation order. Although they are primarily studied to be of practical use...

We give an explicit classification of the arcs in PG(2, q) (q even) with a large conical subset and excess 2, i.e., that consist of q/2 + 1 points of a conic and two points not on that conic. Apart from the initial setup, the methods used are similar to those for the case of odd q, published earlier (Electronic Journal of Combinatorics, 17, #R112).

A small polygon is a convex polygon of unit diameter. We are interested in small polygons which have the largest area for a given number of vertices n. Many instances are already solved in the literature, namely for all odd n, and for n = 4, 6 and 8. Thus, for even n ≥ 10, instances of this problem remain open. Finding those largest small polygons can be formulated as nonconvex quadratic progra...

Let [Formula: see text] be a text]-dimensional quantum polynomial algebra, and central regular element. The quotient algebra is called noncommutative conic. For conic text], there finite-dimensional which determines the singularity of text]. In this paper, we mainly focus on such that its quadratic dual commutative, equivalent to say, determined by symmetric superpotential. We classify these co...