Related papers: Formal Primal-Dual Algorithm Analysis
Today's data-heavy research environment requires the integration of different sources of information into structured data sets that can not be analyzed as simple matrices. We introduce an old technique, known in the European data analyses…
We revisit classic algorithmic search and optimization problems from the perspective of competition. Rather than a single optimizer minimizing expected cost, we consider a zero-sum game in which an optimization problem is presented to two…
We formalise the basics of the double-pushout approach to graph transformation in the proof assistant Isabelle/HOL and provide associated machine-checked proofs. Specifically, we formalise graphs, graph morphisms and rules, and a definition…
We present a formalization of higher-order logic in the Isabelle proof assistant, building directly on the foundational framework Isabelle/Pure and developed to be as small and readable as possible. It should therefore serve as a good…
The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO and have made significant progress. This paper focuses on formal verification,…
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…
We study the problem of minimizing a sum of local objective convex functions over a network of processors/agents. This problem naturally calls for distributed optimization algorithms, in which the agents cooperatively solve the problem…
In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers…
The Adwords and Online Bipartite Matching problems have enjoyed a renewed attention over the past decade due to their connection to Internet advertising. Our community has contributed, among other things, new models (notably stochastic) and…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
An universal primal-dual approach of description equilibriums in large class of hierarchical congestion population games is proposed. At the very core of the approach is hierarchy of enclosed to each other transport networks. In different…
In this paper, we propose an algebraic formalization of the two important classes of dynamic programming algorithms called forward and forward-backward algorithms. They are generalized extensively in this study so that a wide range of other…
We develop stochastic first-order primal-dual algorithms to solve a class of convex-concave saddle-point problems. When the saddle function is strongly convex in the primal variable, we develop the first stochastic restart scheme for this…
We consider online optimization in the 1-lookahead setting, where the objective does not decompose additively over the rounds of the online game. The resulting formulation enables us to deal with non-stationary and/or long-term constraints…
This paper studies online algorithms augmented with multiple machine-learned predictions. While online algorithms augmented with a single prediction have been extensively studied in recent years, the literature for the multiple predictions…
We develop a dynamic version of the primal-dual method for optimization problems, and apply it to obtain the following results. (1) For the dynamic set-cover problem, we maintain an $O(f^2)$-approximately optimal solution in $O(f \cdot \log…
We propose an algorithm-independent framework to equip existing optimization methods with primal-dual certificates. Such certificates and corresponding rate of convergence guarantees are important for practitioners to diagnose progress, in…
We introduce a new theorem prover for classical higher-order logic named auto2. The prover is designed to make use of human-specified heuristics when searching for proofs. The core algorithm is a best-first search through the space of…
The purpose of these notes is to provide background on understanding the primal-dual algorithm of Chambolle and Pock [1] for imaging scientists. The presentation focuses on providing intuition and an algorithmic system that is amenable to…
Autoformalization is the process of automatically translating from natural language mathematics to formal specifications and proofs. A successful autoformalization system could advance the fields of formal verification, program synthesis,…