Related papers: On the duality gap and Gale's example in conic lin…
The generalized trace ratio problem {\rm (GTRP)} is to maximize a quadratic fractional objective function in trace formulation over the Stiefel manifold. In this paper, based on a newly developed matrix S-lemma, we show that {\rm (GTRP)},…
In order to use the Dual Simplex Method, one needs to prove a certain bijection between the dictionaries associated with the primal problem and those associated with its dual. We give a short conceptual proof of why this bijection exists.
Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind:…
Using algebraic methods, and motivated by the one variable case, we study a multipoint interpolation problem in the setting of several complex variables. The duality realized by the residue generator associated with an underlying Gorenstein…
Diese kurze Einfuehrung in Theorie und Berechnung linearer Rekurrenzen versucht, eine Luecke in der Literatur zu fuellen. Zu diesem Zweck sind viele ausfuehrliche Beispiele angegeben. This short introduction to theory and usage of linear…
Geometric programming problem is a powerful tool for solving some special type non-linear programming problems. It has a wide range of applications in optimization and engineering for solving some complex optimization problems. Many…
A sparse linear programming (SLP) problem is a linear programming problem equipped with a sparsity (or cardinality) constraint, which is nonconvex and discontinuous theoretically and generally NP-hard computationally due to the…
Determining the representativeness of a point within a data cloud has recently become a desirable task in multivariate analysis. The concept of statistical depth function, which reflects centrality of an arbitrary point, appears to be…
There is a gap in Theorem 2.2 of the paper of Du (\cite{D_2010}). In this paper, we shall state the gap and repair it.
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
In this article we dwell into the class of so called ill posed Linear Inverse Problems (LIP) in machine learning, which has become almost a classic in recent times. The fundamental task in an LIP is to recover the entire signal / data from…
The purpose of this note is to provide an alternative proof of two quadratic transformation formulas contiguous to that of Gauss using a differential equation approach.
Gauge functions significantly generalize the notion of a norm, and gauge optimization, as defined by Freund (1987}, seeks the element of a convex set that is minimal with respect to a gauge function. This conceptually simple problem can be…
In this paper, we consider the robust linear infinite programming problem $({\rm RLIP}_c) $ defined by \begin{eqnarray*} ({\rm RLIP}_c)\quad &&\inf\; \langle c,x\rangle \textrm{subject to } &&x\in X,\; \langle x^\ast,x \rangle \le r…
We introduce and study a new dual condition which characterizes zero duality gap in nonsmooth convex optimization. We prove that our condition is weaker than all existing constraint qualifications, including the closed epigraph condition.…
We dualize previous work on generalized persistence diagrams for filtrations to cofiltrations. When the underlying space is a manifold, we express this duality as a Poincar\'e duality between their generalized persistence diagrams. A heavy…
The study consists of two parts. Objective of the first part is modern language constructions responsible for algorithmically insolvability of parallelizing problem. Second part contains several ways to modify the constructions to make the…
Duality theorems play a fundamental role in convex optimization. Recently, it was shown how duality theorems for countable probability distributions and finite-dimensional quantum states can be leveraged for building relatively complete…
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…
The work is devoted to the construction of a new interval arithmetic which would combine algorithmic efficiency and high quality estimation of the ranges of expressions.