Duality is an important notion for constrained optimization which provides a theoretical foundation for a number of constraint decomposition schemes such as separable programming and for deriving lower bounds in space decomposition algorithms such as branch and bound. However, the conventional duality theory has the fundamental limit that it leads to duality gaps for nonconvex optimization prob...

We provide a correspondence between the subjects of duality and density in classes of finite relational structures. The purpose of duality is to characterise the structures C that do not admit a homomorphism into a given target B by the existence of a homomorphism from a structure A into C. Density is the order-theoretic property of containing no covers (or ‘gaps’). We show that the covers in t...

This paper studies parameterized stochastic optimization problems in finite discrete time that arise in many applications in operations research and mathematical finance. We prove the existence of solutions and the absence of a duality gap under conditions that relax the boundedness assumption made by Pennanen and Perkkiö in [Stochastic programs without duality gaps, Math. Program., 136(1):91–1...

A class of spectral problems with a hidden Lie-algebraic structure is considered. We define a duality transformation which maps the spectrum of one quasi-exactly solvable (QES) periodic potential to that of another QES periodic potential. The self-dual point of this transformation corresponds to the energy-reflection symmetry found previously for certain QES systems. The duality transformation ...

We derive the probability for rapidity gaps in a parton cascade and investigate the dual connection with hadronic final states. A good description of observations in ee-annihilations is obtained by perturbative QCD calculations in MLLA using previously determined parameters (QCD scale Λ and kT -cut-off Q0) and applying the parton hadron duality picture. Further predictions are derived; especial...

Duality is an important notion for nonlinear programming (NLP). It provides a theoretical foundation for many optimization algorithms. Duality can be used to directly solve NLPs as well as to derive lower bounds of the solution quality which have wide use in other high-level search techniques such as branch and bound. However, the conventional duality theory has the fundamental limit that it le...

The elegant results for strong duality and strict complementarity for linear programming, LP , can fail for cone programming over nonpolyhedral cones. One can have: unattained optimal values; nonzero duality gaps; and no primal-dual optimal pair that satisfies strict complementarity. This failure is tied to the nonclosure of sums of nonpolyhedral closed cones. We take a fresh look at known and ...

Duality theory plays a central role in semidefinite programming, since in optimization algorithms a dual solution serves as a certificate of optimality. However, in semidefinite duality pathological phenomena occur: nonattainment of the optimal value, positive duality gaps, and infeasibility of the dual, even when the primal is bounded. We say that the semidefinite system PSD = {x | ∑m i=1 xiAi...

The concepts of both duality and fuzzy uncertainty in linear programming have been theoretically analyzed, comprehensively and practically applied in an abundance of cases. Consequently, their joint application is highly appealing for both scholars and practitioners. However, the literature contributions on duality in fuzzy linear programming (FLP) are neither complete nor consistent. For examp...