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This work demonstrates the utility of gradients for the global optimization of certain differentiable functions with many suboptimal local minima. To this end, a principle for generating search directions from non-local quadratic…

This paper considers distributed optimization problems, where each agent cooperatively minimizes the sum of local objective functions through the communication with its neighbors. The widely adopted distributed gradient method in solving…

Deep neural networks (DNNs) have shown great success in many machine learning tasks. Their training is challenging since the loss surface of the network architecture is generally non-convex, or even non-smooth. How and under what…

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…

We establish global well-posedness and convergence of the score-based generative models (SGM) under minimal general assumptions of initial data for score estimation. For the smooth case, we start from a Lipschitz bound of the score function…

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…

This paper presents a practical global optimization algorithm for the K-center clustering problem, which aims to select K samples as the cluster centers to minimize the maximum within-cluster distance. This algorithm is based on a…

We prove global convergence in function space for the steepest descent method in shape optimisation with semilinear elliptic partial differential equations. Steepest descent is realized in the Lipschitz topology. In addition, we prove a…

This work aims to solve a stochastic nonconvex nonsmooth composite optimization problem. Previous works on composite optimization problem requires the major part to satisfy Lipschitz smoothness or some relaxed smoothness conditions, which…

In this paper, an efficient modified Newton type algorithm is proposed for nonlinear unconstrianed optimization problems. The modified Hessian is a convex combination of the identity matrix (for steepest descent algorithm) and the Hessian…

This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…

This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…

We study the complexity of producing $(\delta,\epsilon)$-stationary points of Lipschitz objectives which are possibly neither smooth nor convex, using only noisy function evaluations. Recent works proposed several stochastic zero-order…

Current state-of-the-art multi-objective optimization solvers, by computing gradients of all $m$ objective functions per iteration, produce after $k$ iterations a measure of proximity to critical conditions that is upper-bounded by…

Global optimization is a challenging problem, with plenty of algorithms displaying empirical success, but scarce theoretical backing. In this work, we propose a new theoretical framework called Proximal Basin Hopping (PBH), carefully…

A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results.…

A multiscale optimization framework for problems over a space of Lipschitz continuous functions is developed. The method solves a coarse-grid discretization followed by linear interpolation to warm-start project gradient descent on…

In this article we propose a new approach to an analysis of DC optimization problems. This approach was largely inspired by codifferential calculus and the method of codifferential descent and is based on the use of a so-called affine…

This article considers nonconvex global optimization problems subject to uncertainties described by continuous random variables. Such problems arise in chemical process design, renewable energy systems, stochastic model predictive control,…

Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…