. A new proof for this algorithm is presented, based upon the duality of circuits and cuts in a graph. The Blue …-red algorithm is genetic, because the other algorithms can be regarded as special instances. This is shown using the same duality. …

We consider the classical duality operators for convex objects such as the polar of a convex set containing the origin … other duality operators of convex objects. …

This paper attempts to extend the notion of duality for convex cones, by basing it on a predescribed conic ordering and …-product itself is replaced by a general multi-dimensional bilinear mapping. This new type of duality is termed the D-induced duality … in the paper. Basic properties of the extended duality, including the extended bi-polar theorem, are proven. Examples are …

convex cone. In the first half of the paper, we give a detailed study of duality properties of this problem and present … the duality properties of the problem. In the second half of the paper, we propose a self-dual embedding with the … case of strong duality, these objective values in fact converge to the optimal value of the original problem. When the …

This paper presents a unified study of duality properties for the problem of minimizing a linear function over the … intersection of an affine space with a convex cone in finite dimension. Existing duality results are carefully surveyed and some … new duality properties are established. Examples are given to illustrate these new properties. The topics covered in this …

to the development of the duality formulas of convex calculus. This is done by means of one single method: firstly conify … definitions of convex objects, duality operators, binary operations and duality formulas, all without the usual need to exclude … degenerate situations. The duality operator for convex function agrees with the usual one, the Legendre-Fenchel transform, only …

This paper attempts to extend the notion of duality for convex cones, by basing it on a predescribed conic ordering and …-product itself is replaced by a general multi-dimensional bilinear mapping. This new type of duality is termed the D-induced duality … cones and are convenient to use for some practical applications. Properties of the extended duality, including the extended …