Related papers: Generalized Affine Programming & Duality Gap with …
In recent years, information relaxation and duality in dynamic programs have been studied extensively, and the resulted primal-dual approach has become a powerful procedure in solving dynamic programs by providing lower-upper bounds on the…
We introduce an operation on modules over an $F$-finite ring of characteristic $p$. We call this operation \emph{tight interior}. While it exists more generally, in some cases this operation is equivalent to the Matlis dual of tight…
We develop a methodology for closing duality gap and guaranteeing strong duality in infinite convex optimization. Specifically, we examine two new Lagrangian-type dual formulations involving infinitely many dual variables and infinite sums…
The study of polarity in computation has revealed that an "ideal" programming language combines both call-by-value and call-by-name evaluation; the two calling conventions are each ideal for half the types in a programming language. But…
Geoffrion's theorem is a fundamental result from mathematical programming assessing the quality of Lagrangian relaxation, a standard technique to get bounds for integer programs. An often implicit condition is that the set of feasible…
We optimize the running time of the primal-dual algorithms by optimizing their stopping criteria for solving convex optimization problems under affine equality constraints, which means terminating the algorithm earlier with fewer…
We study the problem of super-resolution, where we recover the locations and weights of non-negative point sources from a few samples of their convolution with a Gaussian kernel. It has been recently shown that exact recovery is possible by…
The distribution of prime constellations, such as Twin Primes ($p, p+2$), is traditionally analyzed via probabilistic models or analytic sieve theory. While heuristic predictions are accurate, rigorous proofs are obstructed by the "Parity…
We consider the primal problem of finding the zeros of the sum of a maximally monotone operator with the composition of another maximally monotone operator with a linear continuous operator and a corresponding dual problem formulated by…
We study a commutation pattern in which two affine families commute completely across the two families while each family retains internal noncommutativity. For one-dimensional affine groups over finite commutative rings, we prove a…
The principle of optimality is a fundamental aspect of dynamic programming, which states that the optimal solution to a dynamic optimization problem can be found by combining the optimal solutions to its sub-problems. While this principle…
In this paper we investigate the convergence of a recently popular class of first-order primal-dual algorithms for saddle point problems under the presence of errors occurring in the proximal maps and gradients. We study several types of…
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…
We prove a characterization of profinite algebras, i.e., topological algebras that are isomorphic to a projective limit of finite discrete algebras. In general profiniteness concerns both the topological and algebraic characteristics of a…
Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several…
The aim of this work is to study duality of fractional ideals with respect to a fixed ideal and to investigate the relationship between value sets of pairs of dual ideals in admissible rings, a class of rings that contains the local rings…
The model of asynchronous programming arises in many contexts, from low-level systems software to high-level web programming. We take a language-theoretic perspective and show general decidability and undecidability results for asynchronous…
The main theorem in this paper is a far-reaching generalization of Gleason's theorem on the weight enumerators of codes which applies to arbitrary-genus weight enumerators of self-dual codes defined over a large class of finite rings and…
We extend a primal-dual fixed point algorithm (PDFP) proposed in [5] to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP…
We study online scheduling problems on a single processor that can be viewed as extensions of the well-studied problem of minimizing total weighted flow time. In particular, we provide a framework of analysis that is derived by duality…