Related papers: Duality theory in linear optimization and its exte…
It is shown that there exists a duality among fields. If a field is dual to another field, the solution of the field can be obtained from the dual field by the duality transformation. We give a general result on the dual fields. Different…
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
Methods are described for the solution of linear inference problems subject to deterministic constraints. The approach builds on work by Backus (1970a,b,c) and Parker (1977), but a range useful advances are suggested to address both…
Langrange duality theorems for vector and set optimization problems which are based on an consequent usage of infimum and supremum (in the sense greatest lower and least upper bounds with respect to a partial ordering) have been recently…
In this paper we extend the Tanaka finiteness theorem and inequality for the number of symmetries to arbitrary distributions (differential systems) and provide several applications.
We unify nonlinear Farkas lemma and S-lemma to a generalized alternative theorem for nonlinear nonconvex system. It provides fruitful applications in globally solving nonconvex non-quadratic optimization problems via revealing the hidden…
There is a duality theory connecting certain stochastic orderings between cumulative distribution functions F_1,F_2 and stochastic orderings between their inverses F_1^(-1),F_2^(-1). This underlies some theories of utility in the case of…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
We prove a Ramsey theorem for finite sets equipped with a partial order and a fixed number of linear orders extending the partial order. This is a common generalization of two recent Ramsey theorems due to Soki\'c. As a bonus, our proof…
Based on the complete-lattice approach, a new Lagrangian duality theory for set-valued optimization problems is presented. In contrast to previous approaches, set-valued versions for the known scalar formulas involving infimum and supremum…
In this work we present two particular cases of the general duality result for linear optimisation problems over signed measures with infinitely many constraints in the form of integrals of functions with respect to the decision variables…
A complete first-order theory is equational if every definable set is a Boolean combination of instances of equations, that is, of formulae such that the family of finite intersections of instances has the descending chain condition.…
In this paper we are concerned with a Gordan-type theorem involving an arbitrary number of inequality functions. We not only state its validity under a weak convexity assumption on the functions, but also show it is an optimal result. We…
Sophisticated machine models are increasingly used for high-stakes decisions in everyday life. There is an urgent need to develop effective explanation techniques for such automated decisions. Rule-Based Explanations have been proposed for…
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e. the original problem is first reformulated as a nonconvex optimization problem, its well-posedness…
We associate with each convex optimization problem posed on some locally convex space with an infinite index set T, and a given non-empty family H formed by finite subsets of T, a suitable Lagrangian-Haar dual problem. We provide reverse…
The fundamental duality theories relating algebra and geometry that were discovered in the mid-20th century can also be applied to logic via its algebraization under categorical logic. They thereby result in known and new completeness…
Monadic second order logic is the expansion of first order logic by quantifiers ranging over unary relations. We study the shared monadic second order theory of finite linear orders, i.e. the pseudofinite monadic second order theory of…
Linear complementarity problems provide a powerful framework to model nonsmooth phenomena in a variety of real-world applications. In dynamical control systems, they appear coupled to a linear input-output system in the form of linear…
Most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set. We propose two approaches to impute unspecified…