In this paper we unify divergence minimization and statistical inference by means of convex duality. In the process of doing so, we prove that the dual of approximate maximum entropy estimation is maximum a posteriori estimation. Moreover, our treatment leads to stability and convergence bounds for many statistical learning problems. Finally, we show how an algorithm by Zhang can be used to sol...

Given a T-indistinguishability operator E defined between some fuzzy subsets of a universe of discourse X, this paper studies three ways to generate an indistinguishability operator on X compatible with E inspired by the tools used in approximate reasoning and on the duality principle. Of special interest are the cases when the fuzzy subsets determine a partition and a hard-partition of the uni...

We consider the problem of minimizing an indefinite quadratic function over the nonnegative orthant, or equivalently, the problem of deciding whether a symmetric matrix is copositive. We formulate the problem as a difference of convex functions (d.c.) problem. Using conjugate duality, we show that there is a one-to-one correspondence between their respective stationary points and minima. We the...

1.1 Complementary Slackness: Full and Approximate Recall our canonical linear programs, where x ∈ R, y ∈ R, A ∈ R, b ∈ R, c ∈ R. Primal (P) min cx Ax ≥ b x ≥ 0 Dual (D) max by A y ≤ c y ≥ 0 Also recall that Strong Duality ensures that if both (P) and (D) have finite optima, they are equal. Assume this is the case. Then, for the optima x and y of the primal and dual programs respectively, we hav...

in this paper, we try to determine the status of the relation between dahr world and matrial world. the conclusion shows the subjective duality and objective unity of dahr and material entities. two interpretations of this duality can be suggested. in the first interpretation, this unity, and the duality supposed, are explained on the basis of different intellectual cognition of immaterial and ...

By allocating different information to team members, secret contracts can provide better incentives to perform with an intuitive organizational design. For instance, they may help to monitor monitors, and attain approximately efficient partnerships by appointing a secret principal. More generally, secret contracts highlight a rich duality between enforceability and identifiability. It naturally...

We study gaugino condensation in the presence of an intermediate mass scale in the hidden sector. S-duality is imposed as an approximate symmetry of the effective supergravity theory. Furthermore, we include in the Kähler potential the renormalization of the gauge coupling and the one-loop threshold corrections at the intermediate scale. It is shown that confinement is indeed achieved. Furtherm...

The geometric duality theory of Heyde and Löhne (2006) defines a dual to a multiple objective linear programme (MOLP). In objective space, the primal problem can be solved by Benson’s outer approximation method (Benson, 1998a,b) while the dual problem can be solved by a dual variant of Benson’s algorithm (Ehrgott et al., 2007). Duality theory then assures that it is possible to find the nondomi...

This paper considers a single-cell massive multipleinput multiple-output (MIMO) system equipped with a base station (BS) that uses one-bit quantization and investigates the energy efficiency (EE) and spectral efficiency (SE) trade-off. We first propose a new precoding scheme and downlink power allocation strategy that results in uplink-downlink SINR duality for one-bit MIMO systems. Taking into...