We propose a “cryptographic” interpretation for the propositional connectives of primal infon logic introduced by Y. Gurevich and I. Neeman and prove the corresponding soundness and completeness results. Primal implication φ→p ψ corresponds to the encryption of ψ with a secret key φ, primal disjunction φ ∨p ψ is a group key and ⊥ reflects some backdoor constructions such as full superuser permi...

We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our main analysis technique provides a fresh perspective on Nesterov’s excessive gap technique in a structured fashion and unifies it with smoothing and primal-dual...

Given an integer polyhedron PI ⊂ R, an integer point x̄ ∈ PI , and a point x∗ ∈ R \ PI , the primal separation problem is the problem of finding a linear inequality which is valid for PI , violated by x∗, and satisfied at equality by x̄. The primal separation problem plays a key role in the primal approach to integer programming. In this paper we examine the complexity of primal separation for se...

We propose a family of search directions based on primal-dual entropy in the context of interior point methods for linear programming. This new family contains previously proposed search directions in the context of primal-dual entropy. We analyze the new family of search directions by studying their primal-dual affine-scaling and constant-gap centering components. We then design primal-dual in...

This paper presents a new Lp-primal–dual weak Galerkin (PDWG) finite element method for the div–curl system with normal boundary condition p>1. Two crucial features proposed Lp-PDWG scheme are as follows: (1) it offers an accurate and reliable numerical solution to under low W?,p-regularity (?>0) assumption exact solution; (2) effective approximation of harmonic vector fields on domains complex...

We propose a polynomial time primal dual potential reduction algorithm for linear pro gramming The algorithm generates sequences d and v rather than a primal dual interior point xk sk where di q xi s k i and v k i q xi s k i for i n Only one element of d is changed in each iteration so that the work per iteration is bounded by O mn us ing rank one updating techniques The usual primal dual itera...

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 presents two recurrent neural networks for solving the assignment problem. Simplifying the architecture of a recurrent neural network based on the primal assignment problem, the first recurrent neural network, called the primal assignment network, has less complex connectivity than its predecessor. The second recurrent neural network, called the dual assignment network, based on the ...

We bring together the theories of duality and dynamic programming. We show that the dual of an additively separable dynamic optimization problem can be recursively decomposed using summaries of past Lagrange multipliers as state variables. Analogous to the Bellman decomposition of the primal problem, we prove equality of values and solution sets for recursive and sequential dual problems. In no...

In this paper, we study methods for generating approximate primal solutions as a by-product of subgradient methods applied to the Lagrangian dual of a primal convex (possibly nondifferentiable) constrained optimization problem. Our work is motivated by constrained primal problems with a favorable dual problem structure that leads to efficient implementation of dual subgradient methods, such as ...