A matrix A is called completely positive if it can be decomposed as A = BBT with an entrywise nonnegative matrix B. The set of all such matrices is a convex cone which plays a role in certain optimization problems. A characterization of the interior of this cone is provided.

PURPOSE To simplify the testing of short-wavelength-sensitive (SWS) cone function in the clinic. METHODS SWS-cone discrimination thresholds were measured along the tritan axis using pseudoisochromatic figures displayed on a color monitor. A circular 6 degrees field, containing spatially discrete patches of varying sizes and luminances, was presented on a background. A subset of patches formed...

We consider linear optimization problems over the cone of copositive matrices. Such conic optimization problems, called copositive programs, arise from the reformulation of a wide variety of difficult optimization problems. We propose a hierarchy of increasingly better outer polyhedral approximations to the copositive cone. We establish that the sequence of approximations is exact in the limit....

We consider a primal interior point algorithm for LP. The method uses a search direction obtained by minimizing the original objective over a linearly transformed section of the circular cone circumscribed around the nonnegative orthant. If the latter problem has a finite solution, it provides a lower bound for the optimal objective and a target point specifying a descent direction. Otherwise, ...

By using the the equivalent expression of the second order cone, we reformulate the convex second order cone programming as a boxed constrained optimization, which is a nonlinear programming with four nonnegative constraints. We give the conditions under which the stationary point of the reformulation problem solve the original problem.

The algorithm of Feldkamp, Davis, and Kress [J. Opt. Soc. Am. A 1, 612-619 (1984)] is a widely used filtered-backprojection algorithm for three-dimensional image reconstruction from cone-beam (CB) projections measured with a circular orbit of the x-ray source. A well-known property of this approximate algorithm is that the integral of the reconstructed image along any axial line orthogonal to t...

In this paper we study the relationship between bilevel optimization and multicriteria optimization. Given a bilevel optimization problem, we introduce an order relation such that the optimal solutions of the bilevel problem are the nondominated points with respect to the order relation. In the case where the lower level problem of the bilevel optimization problem is convex and continuously dif...

Two lectins, wheat germ agglutinin (WGA) and peanut agglutinin (PNA), were used to compare domains within the interphotoreceptor matrices (IPM) of the cat and monkey, two species where the morphological relationship between the retinal pigment epithelium (RPE) and photoreceptors is distinctly different. In the monkey, PNA labeling was heaviest over the cone outer segments and a discrete region ...

Error bounds for cone inclusion problems in Banach spaces are established under conditions weaker than Robinson’s constraint qualification. The results allow the cone to be more general than the origin and therefore also generalize a classical error bound result concerning equality-constrained sets in optimization. Applications in finite-dimensional differentiable inequalities and in tangent co...

This paper proposes a convex relaxation of a sparse support vector machine (SVM) based on the perspective relaxation of mixed-integer nonlinear programs. We seek to minimize the zero-norm of the hyperplane normal vector with a standard SVM hinge-loss penalty and extend our approach to a zeroone loss penalty. The relaxation that we propose is a second-order cone formulation that can be efficient...