We obtain several new results for the complex generalized associated Lamé potential V (x) = a(a+ 1)m sn(y,m) + b(b+ 1)m sn(y +K(m),m) +f(f + 1)m sn(y +K(m) + iK ′(m),m) + g(g + 1)m sn(y + iK ′(m),m) , where y ≡ x− K(m) 2 − iK (m) 2 , sn(y,m) is a Jacobi elliptic function with modulus parameter m, and there are four real parameters a, b, f, g. First, we derive two new duality relations which, wh...

In this paper we deal with the minimization of a convex function over the solution set of a range inclusion problem determined by a multivalued operator with convex graph. We attach a dual problem to it, provide regularity conditions guaranteeing strong duality and derive for the resulting primal-dual pair necessary and sufficient optimality conditions. We also discuss the existence of optimal ...

in order to study the effect of canopy gap size on species diversity and composition in mixed stands, a reserved area which located in asalem forests was selected. all of gaps in this area identified and were divided into four categories: small gaps (1000 m2). in each category, 21 of gaps with a relatively homogeneous in terms of an aspect and slope were selected. the major and minor diameter o...

Abstract. We present some new Farkas-type results for inequality systems involving a finite as well as an infinite number of convex constraints. For this, we use two kinds of conjugate dual problems, namely an extended Fenchel-type dual problem and the recently introduced FenchelLagrange dual problem. For the latter, which is a ”combination” of the classical Fenchel and Lagrange duals, the stro...

We study in this paper the strong duality for discrete-time convex constrained portfolio selection problems when adopting a risk neutral computational approach. In contrast to the continuous-time models, there is no known result of the existence conditions in discrete-time models to ensure the strong duality. Investigating the relationship among the primal problem, the Lagrangian dual and the P...

We prove a duality theorem for graded algebras over a field that implies several known duality results: graded local duality, versions of Serre duality for local cohomology and of Suzuki duality for generalized local cohomology, and Herzog-Rahimi bigraded duality.

We consider a financial market with one riskless and one risky asset. The super-replication theorem states that there is no duality gap in the problem of super-replicating a contingent claim under transaction costs and the associated dual problem. We give two versions of this theorem. The first theorem relates a numéraire-based admissibility condition in the primal problem to the notion of a lo...

A gauge function f(.) is a nonnegative convex function that is positively homogeneous and satisfies f(O)=O. Norms and pseudonorms are specific instances of a gauge function. This paper presents a gauge duality theory for a gauge program, which is the problem of minimizing the value of a gauge function f(.) over a convex set. The gauge dual program is also a gauge program, unlike the standard La...