Related papers: Minima distribution for global optimization

For statistical decision problems with finite parameter space, it is well-known that the upper value (minimax value) agrees with the lower value (maximin value). Only under a generalized notion of prior does such an equivalence carry over…

In this paper we consider stochastic composite convex optimization problems with the objective function satisfying a stochastic bounded gradient condition, with or without a quadratic functional growth property. These models include the…

We describe a dynamic programming algorithm for computing the marginal distribution of discrete probabilistic programs. This algorithm takes a functional interpreter for an arbitrary probabilistic programming language and turns it into an…

We study distributed optimization algorithms for minimizing the average of convex functions. The applications include empirical risk minimization problems in statistical machine learning where the datasets are large and have to be stored on…

We propose and analyze asymptotic proximal point (APP) methods to find the global minimizer for a class of nonconvex, nonsmooth, or even discontinuous multiple minima functions. The method is based on an asymptotic representation of…

Distributed optimization often requires finding the minimum of a global objective function written as a sum of local functions. A group of agents work collectively to minimize the global function. We study a continuous-time decentralized…

In this paper, we propose a fully distributed algorithm for second-order continuous-time multi-agent systems to solve the distributed optimization problem. The global objective function is a sum of private cost functions associated with the…

Distributed optimization has gained significant attention in recent years, primarily fueled by the availability of a large amount of data and privacy-preserving requirements. This paper presents a fixed-time convergent optimization…

The divergence minimization problem plays an important role in various fields. In this note, we focus on differentiable and strictly convex divergences. For some minimization problems, we show the minimizer conditions and the uniqueness of…

We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set G up to the smallest possible additive term, called the convergence rate. When the reference set…

In this work, the notions of normal cones at infinity to unbounded sets and limiting and singular subdifferentials at infinity for extended real value functions are introduced. Various calculus rules for these notions objects are…

In this paper we consider general rank minimization problems with rank appearing in either objective function or constraint. We first establish that a class of special rank minimization problems has closed-form solutions. Using this result,…

This paper proposes a novel technique called "successive stochastic smoothing" that optimizes nonsmooth and discontinuous functions while considering various constraints. Our methodology enables local and global optimization, making it a…

This article presents a zeroth order probabilistic global optimization algorithm -- SwiftNav -- for (not necessarily convex) functions over a compact domain. A discretization procedure is deployed on the compact domain, starting with a…

Computing the partition function and the marginals of a global probability distribution are two important issues in any probabilistic inference problem. In a previous work, we presented sub-tree based upper and lower bounds on the partition…

Here, I present a novel method for normalizing a finite set of numbers, which is studied by the domain of biological vision. Normalizing in this context means searching the maximum and minimum number in a set and then rescaling all numbers…

Training neural networks means solving a high-dimensional optimization problem. Normally the goal is to minimize a loss function that depends on what is called the network function, or in other words the function that gives the network…

Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes…

This paper treats the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We present and analyze several different optimality criteria which are based on the notions of stationarity and…

Min-max optimization is emerging as a key framework for analyzing problems of robustness to strategically and adversarially generated data. We propose a random reshuffling-based gradient free Optimistic Gradient Descent-Ascent algorithm for…