Related papers: Minima distribution for global optimization
In model selection problems for machine learning, the desire for a well-performing model with meaningful structure is typically expressed through a regularized optimization problem. In many scenarios, however, the meaningful structure is…
We consider the problem of globally minimizing the sum of many rational functions over a given compact semialgebraic set. The number of terms can be large (10 to 100), the degree of each term should be small (up to 10), and the number of…
We show a connection between global unconstrained optimization of a continuous function $f$ and weak KAM theory for an eikonal-type equation arising also in ergodic control. A solution $v$ of the critical Hamilton-Jacobi equation is built…
We present an optimization algorithm that can identify a global minimum of a potentially nonconvex smooth function with high probability, assuming the Gibbs measure of the potential satisfies a logarithmic Sobolev inequality. Our…
We study the distributed optimization problem over a graphon with a continuum of nodes, which is regarded as the limit of the distributed networked optimization as the number of nodes goes to infinity. Each node has a private local cost…
Loss functions with non-isolated minima have emerged in several machine learning problems, creating a gap between theory and practice. In this paper, we formulate a new type of local convexity condition that is suitable to describe the…
This doctoral thesis is devoted to the analysis of some minimization problems that involve nonlocal functionals. We are mainly concerned with the $s$-fractional perimeter and its minimizers, the $s$-minimal sets. We investigate the behavior…
We introduce a derivative-free global optimization algorithm that efficiently computes minima for various classes of one-dimensional functions, including non-convex, and non-smooth functions.This algorithm numerically approximates the…
An Euler discretization of the Langevin diffusion is known to converge to the global minimizers of certain convex and non-convex optimization problems. We show that this property holds for any suitably smooth diffusion and that different…
In this paper we consider a distributed optimization scenario in which the aggregate objective function to minimize is partitioned, big-data and possibly non-convex. Specifically, we focus on a set-up in which the dimension of the decision…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
This paper is devoted to reduce the conservatism of distributionally robust optimization with moments information. Since the optimal solution of distributionally robust optimization is required to be feasible for all uncertain distributions…
This paper is devoted to second-order variational analysis of a rather broad class of extended-real-valued piecewise liner functions and their applications to various issues of optimization and stability. Based on our recent explicit…
The stochastic composition optimization proposed recently by Wang et al. [2014] minimizes the objective with the compositional expectation form: $\min_x~(\mathbb{E}_iF_i \circ \mathbb{E}_j G_j)(x).$ It summarizes many important applications…
We introduce the proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal convolution formulation. This divergence provides a…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
We propose a new distributed optimization algorithm for solving a class of constrained optimization problems in which (a) the objective function is separable (i.e., the sum of local objective functions of agents), (b) the optimization…
We develop and analyze $M$-estimation methods for divergence functionals and the likelihood ratios of two probability distributions. Our method is based on a non-asymptotic variational characterization of $f$-divergences, which allows the…
In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other…
In this paper, we study the problem of maximizing continuous submodular functions that naturally arise in many learning applications such as those involving utility functions in active learning and sensing, matrix approximations and network…