Related papers: Duality theory in linear optimization and its exte…
Proofs, in Ludics, have an interpretation provided by their counter-proofs, that is the objects they interact with. We follow the same idea by proposing that sentence meanings are given by the counter-meanings they are opposed to in a…
Ultrafinitism postulates that we can only compute on relatively short objects, and numbers beyond certain value are not available. This approach would also forbid many forms of infinitary reasoning and allow to remove certain paradoxes…
The dual character of invariance under transformations and definability by some operations has been used in classical work by for example Galois and Klein. Following Tarski, philosophers of logic have claimed that logical notions themselves…
A set of objects is to be divided fairly among agents with different tastes, modeled by additive utility-functions. If we consider the objects as indivisible, many instances of the decision problem: ``Is there a fair division of the objects…
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…
Dualities are often supposed to be foundational, but they may come into conflict with background independence, because a hidden fixed structures is needed to define the duality transformation. This conflict can be eliminated by extending a…
We review some recent results of the theory of Lie systems in order to apply such results to study Ermakov systems. The fundamental properties of Ermakov systems, i.e. their superposition rules, the Lewis-Ermakov invariants, etc., are found…
We present the proof of the equivalence theorem in quantum field theory which is based on a formulation of this problem in the field-antifield formalism. As an example, we consider a model in which a different choices of natural finite…
We study a theory of asynchronous session types ensuring that well-typed processes terminate under a suitable fairness assumption. Fair termination entails starvation freedom and orphan message freedom namely that all messages, including…
In this paper we look at a class of random optimization problems. We discuss ways that can help determine typical behavior of their solutions. When the dimensions of the optimization problems are large such an information often can be…
Loop-tree duality allows to express virtual contributions in terms of phase-space integrals, thus leading to a direct comparison with real radiation terms. In this talk, we review the basis of the method and describe its application to…
The concept of counterfactual explanations (CE) has emerged as one of the important concepts to understand the inner workings of complex AI systems. In this paper, we translate the idea of CEs to linear optimization and propose, motivate,…
A problem of the erroneous duality gap caused by the presence of symmetries is solved in this paper utilizing point group theory. The optimization problems are first divided into two classes based on their predisposition to suffer from this…
Computational interpretations of linear logic allow static control of memory resources: the data produced by the program are endowed through its type with attributes that determine its life cycle. This has promoted numerous investigations…
Structures based on polarities have been used to provide relational semantics for propositional logics that are modelled algebraically by non-distributive lattices with additional operators. This article develops a first order notion of…
The canonical duality theory has provided with a unified analytic solution to a range of discrete and continuous problems in global optimization, which can transform a nonconvex primal problem to a concave maximization dual problem over a…
Recent works have developed new projection-free first-order methods based on utilizing linesearches and normal vector computations to maintain feasibility. These oracles can be cheaper than orthogonal projection or linear optimization…
The finite satisfiability problem of two-variable logic extended by a linear order successor and a preorder successor is shown to be undecidable.
We develop a unified theory of augmented Lagrangians for nonconvex optimization problems that encompasses both duality theory and convergence analysis of primal-dual augmented Lagrangian methods in the infinite dimensional setting. Our goal…
This paper explores the potential of Lagrangian duality for learning applications that feature complex constraints. Such constraints arise in many science and engineering domains, where the task amounts to learning optimization problems…