Duality in continuous-time homogeneous programming

Continuous-time homogeneous Markov chains

Duality in Homogeneous Programming1

between such functions as u and ü (the representative function agreeing with m on p¡ and approaching u in the norm) the proof runs as follows: From (23), there is, for any e>0, a 50 such that, for §<S0, \\w— 5ä_1M|| <£ where we write Au = w, Sw = u. On multiplying w' = (w — SPu) by Ss one has, from (24) ||Säw —m|| =||Sjh/|| 5SM'||w'|| < M'e which gives (25) and the scheme is convergent. As in P...

Some Duality Results in Grey Linear Programming Problem

Different approaches are presented to address the uncertainty of data and appropriate description of uncertain parameters of linear programming models. One of them is to use the grey systems theory in modeling such problem. Especially, recently, grey linear programming has attracted many researchers. In this paper, a kind of linear programming with grey coefficients is discussed. Introducing th...

Separated Continuous Conic Programming: Strong Duality and an Approximation Algorithm

Motivated by recent applications in robust optimization and in sign-constrained linearquadratic control, we study in this paper a new class of optimization problems called separated continuous conic programming (SCCP). Focusing on a symmetric primal-dual pair, we develop a strong duality theory for the SCCP. Our idea is to use discretization to connect the SCCP and its dual to two ordinary coni...

Duality in nonlinear programming

In this paper are defined new firstand second-order duals of the nonlinear programming problem with inequality constraints. We introduce a notion of a WD-invex problem. We prove weak, strong, converse, strict converse duality, and other theorems under the hypothesis that the problem is WD-invex. We obtain that a problem with inequality constraints is WD-invex if and only if weak duality holds b...