Copositive programming has become a useful tool in dealing with all sorts of optimisation problems. It has however been shown by Murty and Kabadi [K.G. Murty and S.N. Kabadi, Some NP-complete problems in quadratic and nonlinear programming, Mathematical Programming, 39, no.2:117–129, 1987] that the strong membership problem for the copositive cone, that is deciding whether or not a given matrix...

As part of an investigation of the radar backscatter properties of axisymmetric conducting shapes, a study has been made of backscattering by a cone-sphere. This body is comprised of a circular cone with a 25° included cone angle, terminated by a tangent spherical segment. Measurements of backscatter cross sections over all aspect angles are presented for wavelengths in the range from one-tenth...

In this paper we consider the general cone programming problem, and propose primal-dual convex (smooth and/or nonsmooth) minimization reformulations for it. We then discuss first-order methods suitable for solving these reformulations, namely, Nesterov’s optimal method (Nesterov in Doklady AN SSSR 269:543–547, 1983; Math Program 103:127–152, 2005), Nesterov’s smooth approximation scheme (Nester...

The purpose of this study was to evaluate the effects of screwdriver handle shape, surface material and workpiece orientation on torque performance, finger force distribution and muscle activity in a maximum screwdriving torque task. Twelve male subjects performed maximum screw-tightening exertions using screwdriver handles with three longitudinal shapes (circular, hexagonal and triangular), fo...

The positive semideenite constraint for the variable matrix in semideenite programming (SDP) relaxation is further relaxed by a nite number of second order cone constraints in second order cone programming (SOCP) relaxations. A few types of SOCP relaxations are obtained from diierent ways of expressing the positive semideenite constraint of the SDP relaxation. We present how such SOCP relaxatio...

Scalarization of the multiobjective programming problems with fuzzy coefficients using the embedding theorem and the concept of convex cone (ordering cone) is proposed in this paper. Since the set of all fuzzy numbers can be embedded into a normed space, this motivation naturally inspires us to invoke the scalarization techniques in vector optimization problems to evaluate the multiobjective pr...

We develop the Q method for the Second Order Cone Programming problem. The algorithm is the adaptation of the Q method for semidefinite programming originally developed by Alizadeh, Haeberly and Overton, [3] and [2]. We take advantage of the special algebraic structure associated with second order cone programs to formulate the Q method. Furthermore we prove that our algorithm is globally conve...

The objective of this paper is to deal with the fuzzy conic program- ming problems. The aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. Toward this end, The convexity-like concept of fuzzy mappings is introduced and then a speci c ordering cone is established based on the parameterized representation of fuzzy numbers. Un- der this setting, duality t...

With the advent and wide spread use of computers a number of algorithms have been developed to determine the optimum ultimate pit limits in open pit mining. The main objective of these algorithms is to find groups of blocks that should be removed to yield the maximum overall mining profit under specified economic conditions and technological constraints. The most common methods are: Lerchs and ...