Circular programming problems are a new class of convex optimization problems that include second-order cone programming problems as a special case. Alizadeh and Goldfarb [Math. Program. Ser. A 95 (2003) 3-51] introduced primal-dual path-following algorithms for solving second-order cone programming problems. In this paper, we generalize their work by using the machinery of Euclidean Jordan alg...

Abstract In this paper, we present an inexact multiblock alternating direction method for the point-contact friction model of force-optimization problem (FOP). The friction-cone constraints FOP are reformulated as Cartesian product circular cones. We focus on convex quadratic circular-cone programming FOP, which is exact cone-programming model. Coupled with separable objective function, recast ...

Circular programming problems are a new class of convex optimization problems in which we minimize linear function over the intersection of an affine linear manifold with the Cartesian product of circular cones. It has very recently been discovered that, unlike what has previously been believed, circular programming is a special case of symmetric programming, where it lies between second-order ...

Here we formulate second-order cone programs (SOCPs) for synthesizing complex weights for far-field directional (single-point mainbeam) patterns for narrowband arrays. These formulations, while constructed here with the uniform circular array (UCA) in mind, are actually quite general in that they control the arbitrary-pol sidelobe level (SLL) and co-pol SNR loss relative to ideal by minimizing ...

In this paper, we study and analyze the algebraic structure of the circular cone. We establish a new efficient spectral decomposition, set up the Jordan algebra associated with the circular cone, and prove that this algebra forms a Euclidean Jordan algebra with a certain inner product. We then show that the cone of squares of this Euclidean Jordan algebra is indeed the circular cone itself. The...

We present a method to recover a circular truncated cone only from its contour up to a similarity transformation. First, we find the images of circular points, and then use them to calibrate the camera with constant intrinsic parameters from two or three contours of a circular truncated cone, or from a single contour of a circular truncated cylinder. Second, we give an analytical solution of th...

The circular cone Lθ is not self-dual under the standard inner product and includes second-order cone as a special case. In this paper, we focus on the monotonicity of fLθ and circular cone monotonicity of f . Their relationship is discussed as well. Our results show that the angle θ plays a different role in these two concepts.

In this paper, we consider complementarity problem associated with circular cone, which is a type of nonsymmetric cone complementarity problem. The main purpose of this paper is to show the readers how to construct complementarity functions for such nonsymmetric cone complementarity problem, and propose a few merit functions for solving such a complementarity problem. In addition, we study the ...

in this paper, we present a full newton step feasible interior-pointmethod for circular cone optimization by using euclidean jordanalgebra. the search direction is based on the nesterov-todd scalingscheme, and only full-newton step is used at each iteration.furthermore, we derive the iteration bound that coincides with thecurrently best known iteration bound for small-update methods.

Let Lθ be the circular cone in IR which includes second-order cone as a special case. For any function f from IR to IR, one can define a corresponding vector-valued function fLθ on IR by applying f to the spectral values of the spectral decomposition of x ∈ IR with respect to Lθ. The main results of this paper are regarding the Hdifferentiability and calmness of circular cone function fLθ . Spe...