Related papers: Dual Dictionaries in Linear Programming
A bilateralist take on proof-theoretic semantics can be understood as demanding of a proof system to display not only rules giving the connectives' provability conditions but also their refutability conditions. On such a view, then, a…
We consider strongly convex optimization problems with affine-type restrictions. We build dual problem and solve dual problem by Fast Gradient Method. We use primal-dual structure of this method to construct the solution of the primal…
When writing a constraint program, we have to choose which variables should be the decision variables, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables.…
The notion of a two-dimensional word arises naturally in the study of combinatorics on words, while the iterative construction of pedal triangles results in a rich dynamical system in the study of geometry. At first, these two classes of…
This article fits in the area of research that investigates the application of topological duality methods to problems that appear in theoretical computer science. One of the eventual goals of this approach is to derive results in…
In this article we develop a duality principle suitable for a large class of problems in optimization. The main result is obtained through basic tools of convex analysis and duality theory. We establish a correct relation between the…
Given a convex optimization problem and its dual, there are many possible first-order algorithms. In this paper, we show the equivalence between mirror descent algorithms and algorithms generalizing the conditional gradient method. This is…
In this work, we propose a deep neural network architecture motivated by primal-dual splitting methods from convex optimization. We show theoretically that there exists a close relation between the derived architecture and residual…
Classical primal-dual affine programming takes place over finite dimensional real vector spaces. This results in beautiful duality theory, connecting the optimal solu- tions of the primal maximization problem and the dual minimization…
The Kripke semantics of various logics arises via categorical dualities between a category of relational frames and their maps, and a category of algebras and logical homomorphisms. When the relational frames are considered as computational…
For a primal-dual pair of conic linear problems that are described by convex cones $S\subset X$, $T\subset Y$, bilinear symmetric objective functions $\langle\cdot,\cdot\rangle_X$, $\langle\cdot,\cdot\rangle_Y$ and a linear operator…
This paper associates a dual problem to the minimization of an arbitrary linear perturbation of the robust sum function introduced in DOI 10.1007/s11228-019-00515-2. It provides an existence theorem for primal optimal solutions and, under…
Bilevel programming problems frequently arise in real-world applications across various fields, including transportation, economics, energy markets and healthcare. These problems have been proven to be NP-hard even in the simplest form with…
Neural Machine Translation (NMT) has become the new state-of-the-art in several language pairs. However, it remains a challenging problem how to integrate NMT with a bilingual dictionary which mainly contains words rarely or never seen in…
We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…
Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of…
We present a polymorphic linear lambda-calculus as a proof language for second-order intuitionistic linear logic. The calculus includes addition and scalar multiplication, enabling the proof of a linearity result at the syntactic level.
This paper derives a discrete dual problem for a prototypical hybrid high-order method for convex minimization problems. The discrete primal and dual problem satisfy a weak convex duality that leads to a priori error estimates with…
We study propositional logical systems arising from the language of Johansson's minimal logic and obtained by weakening the requirements for the negation operator. We present their semantics as a variant of neighbourhood semantics. We use…
Neural Algorithmic Reasoning (NAR) trains neural networks to simulate classical algorithms, enabling structured and interpretable reasoning over complex data. While prior research has predominantly focused on learning exact algorithms for…