Chandra and Abha [European J. Oper. Res. 122 (2000), 161-165] considered a nonlinear programming problem over cone constraints and presented the correct forms of its four types of duals formulated by Nanda and Das [European J. Oper. Res. 88 (1996) 572-577]. Yang et al. [Indian J. Pure Appl. Math. 35 (2004), 699-708] considered the same problem and discussed weak and strong duality for its four ...

Considering a general vector optimization problem, we attach to it two new vector duals by means of perturbation theory. These vector duals are constructed with the help of the recent Wolfe and Mond-Weir scalar duals for general optimization problems proposed by R.I. Boţ and S.-M. Grad, by exploiting an idea due to W. Breckner and I. Kolumbán. Constrained and unconstrained vector optimization p...

Considering a general optimization problem, we attach to it by means of perturbation theory two dual problems having in the constraints a subdifferential inclusion relation. When the primal problem and the perturbation function are particularized different new dual problems are obtained. In the special case of a constrained optimization problem, the classical Wolfe and Mond–Weir duals, respecti...

In this paper, we will study the relative complexity of the unitary duals of countable groups. In particular, we will explain that if G and H are countable amenable non-type I groups, then the unitary duals of G and H are Borel isomorphic.

Flow type suspension and homotopy suspension agree for attractor-repellor homotopy data. The connection maps associated in Conley index theory to an attractor-repellor decomposition with respect to the direct flow and its inverse are SpanierWhitehead duals in the stably parallelizable context and are duals modulo a certain Thom construction in general.

It is well known that a plane graph is Eulerian if and only if its geometric dual is bipartite. We extend this result to partial duals of plane graphs. We then characterize all bipartite partial duals of a plane graph in terms of oriented circuits in its medial graph.

We present a new linear time algorithm for nding rectangular duals of planar triangular graphs. The algorithm is conceptually simpler than the previous known algorithm. The coordinates of the rectangular dual constructed by our algorithm are integers and have pure combinatorial meaning. This allows us to discuss the heuristics for minimizing the size of the rectangular duals.

Report The aim of this work is to make some investigations concerning duality for mul-tiobjective optimization problems. In order to do this we study first the duality for scalar optimization problems by using the conjugacy approach. This allows us to attach three different dual problems to a primal one. We examine the relations between the optimal objective values of the duals and verify, unde...