Related papers: Duality theory in linear optimization and its exte…

This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…

We show that Lurie's results on Tannaka duality for geometric stacks hold without any tameness hypotheses. We deduce this as a consequence of an affineness theorem in the theory of sheaves of categories. This affineness result is also…

We argue that the finiteness of quantum gravity amplitudes in fully compactified theories (at least in supersymmetric cases) leads to a bottom-up prediction for the existence of non-trivial dualities. In particular, finiteness requires the…

We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…

From the method of realization of bialgebras developped in a preceding paper, we obtain the Duality Theorem and apply it to the study of the ideal of relations for each realized bialgebra. This is detailed in the english version of the…

The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…

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…

General nonconvex optimization problems are studied by using the canonical duality-triality theory. The triality theory is proved for sums of exponentials and quartic polynomials, which solved an open problem left in 2003. This theory can…

We deal with the monadic (second-order) theory of order. We prove all known results in a unified way, show a general way of reduction, prove more results and show the limitation on extending them. We prove (CH) that the monadic theory of…

We prove the sufficiency of the Linear Superposition Principle for linear trees, which characterizes the spectra achievable by a real symmetric matrix whose underlying graph is a linear tree. The necessity was previously proven in 2014.…

Using exhaustion method and finite differences a new method to solve system of partial differential equations and is presented. This method allows design algorithm to solve linear and nonlinear systems in irregular domains. Applying this…

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…

We introduce a new way of quantifying the degrees of incompatibility of two ob- servables in a probabilistic physical theory and, based on this, a global measure of the degree of incompatibility inherent in such theories, across all…

We provide an exact algorithm to solve the log-linear continuous (fractional) knapsack problem. The algorithm is based on two lemmas that follow from the application of weak duality theorem and complementary slackness theorem to the linear…

Starting from lagrangian field theory and the variational principle, we show that duality in equations of motion can also be obtained by introducing explicit spacetime dependence of the lagrangian. Poincare invariance is achieved precisely…

Diversities are an extension of the concept of a metric space which assign a non-negative value to every finite set of points, rather than just pairs. A general theory of diversities has been developed which exhibits many deep analogies to…

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…

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…

For a linear difference equation with the coefficients being computable sequences, we establish algorithmic undecidability of the problem of determining the dimension of the solution space including the case when some additional prior…

A linear constraint loop is specified by a system of linear inequalities that define the relation between the values of the program variables before and after a single execution of the loop body. In this paper we consider the problem of…