In this paper, we will present a multitude of global semiparametric sufficient efficiency conditions under various generalized ( ,b,φ,ρ,θ)-univexity hypotheses for the following multiobjective fractional subset programming problem: (P) Minimize(F1(S)/G1(S),F2(S)/G2(S), . . . ,Fp(S)/Gp(S)) subject to Hj(S) 0, j ∈ q, S∈An, where An is the n-fold product of the σ-algebra A of subsets of a given se...

We give some new regularity conditions for Fenchel duality in separated locally convex vector spaces, written in terms of the notion of quasi interior and quasi-relative interior, respectively. We provide also an example of a convex optimization problem for which the classical generalized interior-point conditions given so far in the literature cannot be applied, while the one given by us is ap...

In this paper we explore the relations between the standard dual problem of a convex generalized fractional programming problem and the “partial” dual problem proposed by Barros et al. (1994). Taking into account the similarities between these dual problems and using basic duality results we propose a new algorithm to directly solve the standard dual of a convex generalized fractional programmi...

We present a conjugate duality approach for multifacility minimax location problems with geometric constraints, where the underlying space is Fréchet and the distances are measured by gauges of closed convex sets. Besides assigning corresponding conjugate dual problems, we derive necessary and sufficient optimality conditions. Moreover, we introduce a further dual problem with less dual variabl...

Recently S.A. Clark published an interesting duality result in linear conic programming dealing with a convex cone that is not closed in which the usual (algebraic) dual problem is replaced by a topological dual with the aim to have zero duality gap under certain usual hypotheses met in mathematical finance. We present some examples to show that an extra condition is needed for having the concl...

We consider Continuous Linear Programs over a continuous finite time horizon T , with linear cost coefficient functions and linear right hand side functions and a constant coefficient matrix, where we search for optimal solutions in the space of measures or of functions of bounded variation. These models generalize the Separated Continuous Linear Programming models and their various duals, as f...

This paper develops the deterministic approach to duality for semi-definite linear programming problems in the face of data uncertainty. We establish strong duality between the robust counterpart of an uncertain semi-definite linear programming model problem and the optimistic counterpart of its uncertain dual. We prove that strong duality between the deterministic counterparts holds under a ch...

Stone-type duality connects logic, algebra, and topology in both conceptual and technical senses. This paper is intended to be a demonstration of this slogan. In this paper we focus on some versions of Fitting’s L-valued logic and L-valued modal logic for a finite distributive lattice L. Using the theory of natural dualities, we first obtain a duality for algebras of L-valued logic. Based on th...

Lagrangian duality underlies many efficient algorithms for convex minimization problems. A key ingredient is strong duality. Lagrangian relaxation also provides lower bounds for non-convex problems, where the quality of the lower bound depends on the duality gap. Quadratically constrained quadratic programs (QQPs) provide important examples of non-convex programs. For the simple case of one qua...

Daniel Green, Albion Lawrence, John McGreevy, David R. Morrison, and Eva Silverstein SLAC and Department of Physics, Stanford University, Stanford, CA 94305-4060 Brandeis Theory Group, Brandeis University, MS 057, PO Box 549110, Waltham, MA 02454 Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 Center for Geometry and Theoretical Physics, Duke Universit...