Related papers: Foundations of gauge and perspective duality
This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is a new parameterization of the optimality condition which allows us to…
The problem of maintaining scale and conformal invariance in Maxwell and general N-form gauge theories away from their critical dimension d=2(N+1) is analyzed.We first exhibit the underlying group-theoretical clash between…
We prove a duality relation and an integration by parts formula for fractional operators with a general analytical kernel. Based on these basic results, we are able to prove a new Gronwall's inequality and continuity and differentiability…
We study a gauge/gravity model for the thermodynamics of a gauge theory with one running coupling. The gravity side contains an ansatz for the metric and a scalar field, on the field theory side one starts by giving an ansatz for the beta…
Non-convex functional constrained optimization problems have gained substantial attention in machine learning and data science, addressing broad requirements that typically go beyond the often performance-centric objectives. An influential…
A key idea in convex optimization theory is to use well-structured affine functions to approximate general functions, leading to impactful developments in conjugate functions and convex duality theory. This raises the question: what are the…
We introduce a compositional framework for convex analysis based on the notion of convex bifunction of Rockafellar. This framework is well-suited to graphical reasoning, and exhibits rich dualities such as the Legendre-Fenchel transform,…
Although the introduction of generalised and extended geometry has been motivated mainly by the appearance of dualities upon reductions on tori, it has until now been unclear how (all) the duality transformations arise from first principles…
This paper studies distributed convex optimization with both affine equality and nonlinear inequality couplings through the duality analysis. We first formulate the dual of the coupling-constraint problem and reformulate it as a consensus…
A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In spite of being an integral part of bundle adjustment and…
The consistent description of unstable particles, renormalons, or other Schwinger--Dyson-type of solutions within the framework of perturbative gauge field theories necessitates the definition and resummation of off-shell Green's functions,…
We expand the generic model involving chiral matter, super Yang-Mills gauge fields, and supergravity to second order in the gravity and gauge prepotentials in a manifestly covariant and conformal way. Such a class of models includes…
This work studies the strong duality of non-convex matrix factorization problems: we show that under certain dual conditions, these problems and its dual have the same optimum. This has been well understood for convex optimization, but…
This paper derives a discrete dual problem for a prototypical hybrid high-order method for convex minimization problems. The discrete primal and dual problem satisfy a weak convex duality that leads to a priori error estimates with…
In this paper we study the asymptotic behaviour of the solutions of some minimization problems for integral functionals with convex integrands, in two-dimensional domains with cracks, under perturbations of the cracks in the Hausdorff…
A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…
We extend the duality principle for the $\Gamma$-convergence of convex lower semicontinuous functions, which was previously established only in separable reflexive Banach spaces, to the broader class of weakly compactly generated (WCG)…
The partition functions of refined topological strings(A-models) are computed, which give rise to the circle-compactified five-dimensional supersymmetric linear quiver gauge theories in generic (not necessarily self-dual) Omega backgrounds.…
Generalized moment problems optimize functional expectation over a class of distributions with generalized moment constraints, i.e., the function in the moment can be any measurable function. These problems have recently attracted growing…
A dual foliation treatment of General Relativity is presented. The basic idea of the construction is to consider two foliations of a spacetime by spacelike hypersurfaces and relate the two geometries. The treatment is expected to be useful…