Related papers: Duality for Sudoku
We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality…
We consider the convex bilevel optimization problem, also known as simple bilevel programming. There are two challenges in solving convex bilevel optimization problems. Firstly, strong duality is not guaranteed due to the lack of Slater…
This article develops a primal dual formulation for a primal proximal approach suitable for a large class of non-convex models in the calculus of variations. The results are established through standard tools of functional analysis, convex…
Extending the investigations about the theory of duals, we analyze duals built up with the aid of discrete symmetry operators. We scrutinize algebraic and physical constraints (encompassing them in a theoretical scope) in order to verify…
Two actively researched problem settings in matchings under preferences are popular matchings and the three-dimensional stable matching problem with cyclic preferences. In this paper, we apply the optimality notion of the first topic to the…
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…
We study the interplay between T-duality, compactification and supersymmetry. We prove that when the original configuration has unbroken space-time supersymmetries, the dual configuration also does if a special condition is met: the Killing…
A recent line of research investigates how algorithms can be augmented with machine-learned predictions to overcome worst case lower bounds. This area has revealed interesting algorithmic insights into problems, with particular success in…
Duality of curves is one of the important aspects of the ``classical'' algebraic geometry. In this paper, using this foundation, the duality of tropical polynomials is constructed to introduce the duality of Non-Archimedean curves. Using…
Density function describes the density of states in the state space of a dynamic system or a Markov Decision Process (MDP). Its evolution follows the Liouville equation. We show that the density function is the dual of the value function in…
A general primal-dual splitting algorithm for solving systems of structured coupled monotone inclusions in Hilbert spaces is introduced and its asymptotic behavior is analyzed. Each inclusion in the primal system features compositions with…
The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…
In this paper we derive robust super- and subhedging dualities for contingent claims that can depend on several underlying assets. In addition to strict super- and subhedging, we also consider relaxed versions which, instead of eliminating…
For the existence of strong duality in convex optimization regularity conditions play an indisputable role. We mainly deal in this paper with regularity conditions formulated by means of different generalizations of the notion of interior…
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…
The paper deals with the optimal control problem described by second order evolution differential inclusions; to this end first we use an auxiliary problem with second order discrete and discrete-approximate inclusions. Then applying…
Binary optimization is a powerful tool for modeling combinatorial problems, yet scalable and theoretically sound solution methods remain elusive. Conventional solvers often rely on heuristic strategies with weak guarantees or struggle with…
We investigate quantitative extensions of modal logic and the modal mu-calculus, and study the question whether the tight connection between logic and games can be lifted from the qualitative logics to their quantitative counterparts. It…
The solutions that describe the motion of the classical simple pendulum have been known for very long time and are given in terms of elliptic functions, which are doubly periodic functions in the complex plane. The independent variable of…
We revisit the foundations of gauge duality and demonstrate that it can be explained using a modern approach to duality based on a perturbation framework. We therefore put gauge duality and Fenchel-Rockafellar duality on equal footing,…