A generally nonconvex optimization problem with equality constraints is studied. The problem is introduced as an “inf sup” of a generalized augmented Lagrangian function. A dual problem is defined as the “sup inf’ of the same generalized augmented Lagrangian. Sufftcient conditions are derived for constructing the augmented Lagrangian function such that the extremal values of the primal and dual...

Lee in 1970 determined the equational subclasses m B of the class of all pseudo complemented lattices. Then many authors have worked with the lattices which are in m B , sectionally in m B and relatively in m B . In this paper we extend some of their results in terms of n-ideals. We will study those ( ) L Fn which are relatively in m B . Here we include a number of characterizations of those ( ...

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 ...

We generalize primal-dual interior-point methods for linear programming problems to the convex optimization problems in conic form. Previously, the most comprehensive theory of symmetric primal-dual interior-point algorithms was given by Nesterov and Todd 8, 9] for the feasible regions expressed as the intersection of a symmetric cone with an aane subspace. In our setting, we allow an arbitrary...

We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in [21] for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators involved we obtain for the sequences of iterates that approach the solution orders of convergence of O( 1 n) and O(ωn), for ω ∈ (0, 1), respectively. The investigate...

In the last lecture we saw how to formulate a dual program for an optimization problem. From the formulation, it turned out that the dual program gave an upper/lower bound depending on whether the problem was maximization/minimization respectively. Today, the focus will be on when are these bounds tight. It turns out that these bounds are tight in most of the cases of interest like linear progr...

in this paper, we introduce and study the prime, strongly prime,semiprime and irreducible fuzzy bi-ideals of a semigroup. we characterize thosesemigroups for which each fuzzy bi-ideal is semiprime. we also characterizethose semigroups for which each fuzzy bi-ideal is strongly prime.

Minimum cost flow problems in infinite networks arise, for example, in infinite-horizon sequential decision problems such as production planning. Strong duality for these problems was recently established for the special case of linear costs using an infinite-dimensional simplex algorithm. Here, we use a different approach to derive duality results when the costs are convex. We formulate the pr...