Related papers: Gauge optimization and duality
Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
The canonical duality theory has provided with a unified analytic solution to a range of discrete and continuous problems in global optimization, which can transform a nonconvex primal problem to a concave maximization dual problem over a…
This paper is concerned with the study of constrained statistical learning problems, the unconstrained version of which are at the core of virtually all of modern information processing. Accounting for constraints, however, is paramount to…
This paper presents a theory of optimization fabrics, second-order differential equations that encode nominal behaviors on a space and can be used to define the behavior of a smooth optimizer. Optimization fabrics can encode commonalities…
Recently, a new class of non-convex optimization problems motivated by the statistical problem of learning an acyclic directed graphical model from data has attracted significant interest. While existing work uses standard first-order…
This paper studies duality and optimality conditions for general convex stochastic optimization problems. The main result gives sufficient conditions for the absence of a duality gap and the existence of dual solutions in a locally convex…
We study dual-based algorithms for distributed convex optimization problems over networks, where the objective is to minimize a sum $\sum_{i=1}^{m}f_i(z)$ of functions over in a network. We provide complexity bounds for four different…
General nonconvex optimization problems are studied by using the canonical duality-triality theory. The triality theory is proved for sums of exponentials and quartic polynomials, which solved an open problem left in 2003. This theory can…
This paper proposes a universal algorithm for convex minimization problems of the composite form $g_0(x)+h(g_1(x),\dots, g_m(x)) + u(x)$. We allow each $g_j$ to independently range from being nonsmooth Lipschitz to smooth, from convex to…
In this paper, we provide a mathematical framework for improving generalization in a class of learning problems which is related to point estimations for modeling of high-dimensional nonlinear functions. In particular, we consider a…
This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity guarantees and practical performance. The method contains elements of two existing methods: the…
Taking into account the recent developments associated with duality in physics, this article is focused on investigating the properties of a tensor generalization of the electrodynamics dual to the standard vector model even considering the…
We investigate Lagrangian duality for nonconvex optimization problems. To this aim we use the $\Phi$-convexity theory and minimax theorem for $\Phi$-convex functions. We provide conditions for zero duality gap and strong duality. Among the…
We present a general convex relaxation approach to study a wide class of Unbalanced Optimal Transport problems for finite non-negative measures with possibly different masses. These are obtained as the lower semicontinuous and convex…
Duality symmetries of supergravity theories are powerful tools to restrict the number of possible actions, to link different dimensions and number of supersymmetries and might help to control quantisation. (Hodge-Dirac-)Dualisation of gauge…
Let $d$ and $k$ be positive integers. Let $\mu$ be a positive Borel measure on $\mathbb{R}^2$ possessing finite moments up to degree $2d-1$. If the support of $\mu$ is contained in an algebraic curve of degree $k$, then we show that there…
Gauge/gravity duality is the conjecture that string theories have dual descriptions as gauge theories. Weakly-coupled gravity is dual to strongly-coupled gauge theories, ideal for lattice calculations. I will show precision lattice…
The aim of structured optimization is to assemble a solution, using a given set of (possibly uncountably infinite) atoms, to fit a model to data. A two-stage algorithm based on gauge duality and bundle method is proposed. The first stage…
In many real world problems, optimization decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of points…