We give new regularity conditions based on epigraphs that assure strong duality between a given primal convex optimization problem and its Lagrange and Fenchel-Lagrange dual problems, respectively, in infinite dimensional spaces. Moreover we completely characterize through equivalent statements the so-called stable strong duality between the initial problem and the mentioned duals.

this paper consider the   general  forms of $(alpha,beta)$-fuzzyleft ideals (right ideals, bi-ideals, interior ideals) of an orderedsemigroup, where$alpha,betain{in_{gamma},q_{delta},in_{gamma}wedgeq_{delta}, in_{gamma}vee q_{delta}}$ and $alphaneqin_{gamma}wedge q_{delta}$. special attention is paid to$(in_{gamma},ivq)$-left ideals (right ideals, bi-ideals, interiorideals) and some related  pr...

the verse on “the world of primal covenant (‘alam al-zarr)” is among difficult quranic verses whose difficulty can be discovered by consideration of different opinions, which are sometimes opposite to one another, presented by quranic commentators. having accepted the existence of “the world of primal covenant,” mulla sadra has interpreted and expounded that world in accordance with his philoso...

The ideals generated by the minors of matrices whose entries are linear forms are not yet well-understood, unless the forms themselves satisfy some strong condition. One has a wealth of information if the matrix is generic, symmetric generic or Hankel; here we tackle 1-generic matrices. We recall the definition of 1-genericity introduced in [E2] by Eisenbud: Let F be a field and X1, . . . , Xs ...

We investigate a variation of the transitivity problem for proximinality properties of subspaces and intersection properties of balls in Banach spaces. For instance, we prove that if Z ⊆ Y ⊆ X, where Z is a finite co-dimensional subspace of X which is strongly proximinal in Y and Y is an M -ideal in X, then Z is strongly proximinal in X. Towards this, we prove that a finite co-dimensional proxi...

We study the polyhedral structure of two primal relaxations of a class of specially structured mixed integer programming problems. This class includes the generalized capacitated plant location problem and a production scheduling problem as special cases. We show that for this class of problems two polyhedra constructed from the constraint sets in two difl‘erent primal relaxations are identical...

We provide a unifying geometric framework for the analysis of general classes of duality schemes and penalty methods for nonconvex constrained optimization problems. We present a separation result for nonconvex sets via general concave surfaces. We use this separation result to provide necessary and sufficient conditions for establishing strong duality between geometric primal and dual problems...

In this work we study the duality for a general multiobjective optimization problem. Considering, first, a scalar problem, different duals using the conjugacy approach are presented. Starting from these scalar duals, we introduce six different multiobjective dual problems to the primal one, one depending on certain vector parameters. The existence of weak and, under certain conditions, of stron...