Related papers: Gauge optimization and duality
Gauges, or convex distance functions are, roughly speaking, norms without symmetry. In this paper we intend to quantify how asymmetric a planar gauge can be. We introduce asymmetry measures for smooth gauges and for strictly convex gauges,…
Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterization methods for convex objects and applications in image…
In this paper, we consider the algorithms and convergence for a general optimization problem, which has a wide range of applications in image segmentation, topology optimization, flow network formulation, and surface reconstruction. In…
This note focuses the problem of motivating the use of gauge symmetries (being the identity on the observables) from general principles, beyond their practical success, starting from global gauge symmetries and then by emphasizing the…
We introduce topological gauge fields as nontrivial field configurations enforced by topological currents. These fields crucially determine the form of statistical gauge fields that couple to matter and transmute their statistics. We…
There is considered an extension of gauge theories according to the assumption of a generalized uncertainty principle which implies a minimal length scale. A modification of the usual uncertainty principle implies an extended shape of…
The main purpose of this research note is to show that the triality theory can always be used to identify both global minimizer and the biggest local maximizer in global optimization. An open problem left on the double-min duality is solved…
Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For…
A unified model is addressed for general optimization problems in multi-scale complex systems. Based on necessary conditions and basic principles in physics, the canonical duality-triality theory is presented in a precise way to include…
We consider a gauge theory action for continuous spin particles formulated in a spacetime enlarged by an extra coordinate recently proposed by Schuster and Toro. It requires one scalar gauge field and has two local symmetries. We show that…
Weak optimal transport generalizes the classical theory of optimal transportation to nonlinear cost functions and covers a range of problems that lie beyond the traditional theory - including entropic transport, martingale transport, and…
By applying the perturbation function approach, we propose the Lagrangian and the conjugate duals for minimization problems of the sum of two, generally nonconvex, functions. The main tools are the $\Phi$-convexity theory and minimax…
This paper studies a multiobjective bilevel optimization problem where each objective is a fractional function. By reformulating the problem into a single-level one, we establish refined necessary and sufficient optimality conditions. These…
We study geodesically convex (g-convex) problems that can be written as a difference of Euclidean convex functions. This structure arises in several optimization problems in statistics and machine learning, e.g., for matrix scaling,…
In this paper, we explore the algebraic and geometric structures that arise from a procedure we dub "gauging the gauge", which involves the promotion of a certain global, coordinate independent symmetry to a local one. By gauging the global…
In this paper, a new optimization framework is defined that includes the optimization framework recently proposed in [1]-[2] as a special case. The convex optimization in [1]-[2] includes centralized optimization and distributed…
We consider the problem of predicting the covariance of a zero mean Gaussian vector, based on another feature vector. We describe a covariance predictor that has the form of a generalized linear model, i.e., an affine function of the…
The present article is dedicated to proving convergence of the stochastic gradient method in case of random shape optimization problems. To that end, we consider Bernoulli's exterior free boundary problem with a random interior boundary. We…
In this paper, we obtain results about the positive definiteness, the continuity and the level-boundedness of two optimal value functions of specific parametric optimization problems. Those two optimization problems are generalizations of…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…