In this paper, we describe a conic approach to the stability theory of uncertain polynomials. We present necessary and sufficient conditions for a conic set p0 + K of polynomials to be Hurwitz stable (K is a convex cone of polynomials of degree ≤ n and deg p0 = n). As analytical tools we derive an edge theorem and Rantzer type conditions for marginal stability (semi-stability). The results are ...

The paper considers solving of linear programming problems with p-order conic constraints that are related to a certain class of stochastic optimization models with risk objective or constraints. The proposed approach is based on construction of polyhedral approximations for p-order cones, and then invoking a Benders decomposition scheme that allows for efficient solving of the approximating pr...

We discuss natural connections between three objects: quadratic forms with values in line bundles, conic bundles and quaternion orders. We use the even Clifford algebra, and the Brauer-Severi Variety, and other constructions to give natural bijections between these objects under appropriate hypothesis. We then restrict to a surface base and we express the second Chern class of the order in term...

Inspired by the principle of satisficing (Simon 1955), Long et al. (2021) propose an alternative framework for optimization under uncertainty, which we term as a robust model. Instead sizing uncertainty set in optimization, model is specified target objective with aim delivering solution that least impacted achieving target. At heart this framework, minimize level constraint violation all possi...

Structured light is a perception method that allows us to obtain 3D information from images of the scene by projecting synthetic features with a light emitter. Traditionally, this method considers a rigid configuration, where the position and orientation of the light emitter with respect to the camera are known and calibrated beforehand. In this paper we propose a new omnidirectional structured...

In the Bézier formalism, an arc of a conic is a rational curve of degree 2 with control polygon {P, Q, R} for which the weights can be normalized to {1, w, 1}. The parametrization of the conic arc is C(t) = (1 − t) 2 P + 2wt(1 − t)Q + t 2 R (1 − t) 2 + 2wt(1 − t) + t 2 , t ∈ [0, 1]. Abstract Synthetic derivation of closed for-mulae of the geometric characteristic of a conic given in Bézier form...

We consider scalarization issues for vector problems in the case where the preference relation is represented by a rather arbitrary set. An algorithm for weights choice for a priori unknown preference relations is suggested. Some examples of applications to vector optimization, game equilibrium, and variational inequalities are described. DOI: 10.3103/S1066369X12090022

This paper presents a practical representation containing a parameter of rational cubic conic sections and research’s deeply the inner properties. Firstly, the parameter how to affect the control points, inner weights and shoulder point is discussed. Secondly, the inner relation between the parameter and the weights of the nonstandard-form quadratic rational conic sections is analyzed in detail...