Second-order necessary optimality conditions for nonlinear conic programming problems that depend on a single Lagrange multiplier are usually built under nondegeneracy and strict complementarity. In this paper we establish condition of such type two classes problems, namely semidefinite second-order cone programming, assuming Robinson’s constraint qualification weak constant rank-type property ...

The constant rank constraint qualification, introduced by Janin in 1984 for nonlinear programming, has been extensively used sensitivity analysis, global convergence of first- and second-order algorithms, computing the directional derivative value function. In this paper we discuss naive extensions rank-type qualifications to cone programming semidefinite which are based on Approximate-Karush–K...

We are given a finite set of m points (guards) G in the plane R 2 and an angle 0 ≤ Θ ≤ 2π. A Θ-cone is a cone with apex angle Θ. We call a Θ-cone empty (with respect to G) if it does not contain any point of G. A point p ∈ R is called Θ-guarded if every Θ-cone with apex located at p is non-empty. Moreover, the set of all Θ-guarded points is called Θ-region. We first show how to construct a data...

Image reconstruction from cone-beam projections collected along a single circular source trajectory is commonly done using the Feldkamp algorithm, which performs well only with a small cone angle. In this report, we propose an error-reduction-based algorithm to increase the cone angle by several folds to achieve satisfactory image quality at the same radiation dose. In our scheme, we first reco...

We consider convex programming problems in a canonical homogeneous format, a very general form of Karmarkar’s canonical linear programming problem. More specifically, by homogeneous programming we shall refer to the problem of testing if a homogeneous convex function has a nontrivial zero over a subspace and its intersection with a pointed convex cone. To this canonical problem, endowed with a ...

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY Linear Project Second Order-Cone Programme Zhenhua Li, Wenling Zhao *1,2 School of Science,Shandong University of Technology, Zibo,255091,China [email protected] Abstract In recent years cone constraint optimization problems has been favored by scholars, especially for the second-order cone constraints programming problem,the...

We propose the moment cone relaxation for a class of polynomial optimization problems (POPs) to extend the results on the completely positive cone programming relaxation for the quadratic optimization (QOP) model by Arima, Kim and Kojima. The moment cone relaxation is constructed to take advantage of sparsity of the POPs, so that efficient numerical methods can be developed in the future. We es...

We propose the moment cone relaxation for a class of polynomial optimization problems (POPs) to extend the results on the completely positive cone programming relaxation for the quadratic optimization (QOP) model by Arima, Kim and Kojima. The moment cone relaxation is constructed to take advantage of sparsity of the POPs, so that efficient numerical methods can be developed in the future. We es...

We studied the spatial arrangement of L- and M-cone driven electroretinograms (ERGs) reflecting the activity of magno- and parvocellular pathways. L- and M-cone isolating sine wave stimuli were created with a four primary LED stimulator using triple silent substitution paradigms. Temporal frequencies were 8 and 12 Hz, to reflect cone opponent activity, and 30, 36 and 48 Hz to reflect luminance ...