Related papers: First-order optimization on stratified sets
In this paper, we study optimization methods consisting of iteratively minimizing surrogates of an objective function. By proposing several algorithmic variants and simple convergence analyses, we make two main contributions. First, we…
In this study, we consider an optimization problem with uncertainty dependent on decision variables, which has recently attracted attention due to its importance in machine learning and pricing applications. In this problem, the gradient of…
First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…
Invex programs are a special kind of non-convex problems which attain global minima at every stationary point. While classical first-order gradient descent methods can solve them, they converge very slowly. In this paper, we propose new…
This work concerns the analysis and design of distributed first-order optimization algorithms over time-varying graphs. The goal of such algorithms is to optimize a global function that is the average of local functions using only local…
We consider a class of popular distributed non-convex optimization problems, in which agents connected by a network $\mathcal{G}$ collectively optimize a sum of smooth (possibly non-convex) local objective functions. We address the…
In this paper we develop accelerated first-order methods for convex optimization with locally Lipschitz continuous gradient (LLCG), which is beyond the well-studied class of convex optimization with Lipschitz continuous gradient. In…
We consider high order approximations of the solution of the stochastic filtering problem, derive their pathwise representation in the spirit of the earlier work of Clark and Davis and prove their robustness property. In particular, we show…
We study the problem of minimizing a sum of local objective convex functions over a network of processors/agents. This problem naturally calls for distributed optimization algorithms, in which the agents cooperatively solve the problem…
We consider the minimization of an $L_0$-Lipschitz continuous and expectation-valued function, denoted by $f$ and defined as $f(x)\triangleq \mathbb{E}[\tilde{f}(x,\omega)]$, over a Cartesian product of closed and convex sets with a view…
We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly non differentiable, function. The key features of the proposed method are the definition of a…
We investigate the continuous non-monotone DR-submodular maximization problem subject to a down-closed convex solvable constraint. Our first contribution is to construct an example to demonstrate that (first-order) stationary points can…
The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…
This paper proposes low-complexity algorithms for finding approximate second-order stationary points (SOSPs) of problems with smooth non-convex objective and linear constraints. While finding (approximate) SOSPs is computationally…
In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function whose gradient is…
This paper considers a distributed stochastic non-convex optimization problem, where the nodes in a network cooperatively minimize a sum of $L$-smooth local cost functions with sparse gradients. By adaptively adjusting the stepsizes…
Stochastic coordinate descent algorithms are efficient methods in which each iterate is obtained by fixing most coordinates at their values from the current iteration, and approximately minimizing the objective with respect to the remaining…
We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle:…
We prove the first convergence guarantees for a subgradient method minimizing a generic Lipschitz function over generic Lipschitz inequality constraints. No smoothness or convexity (or weak convexity) assumptions are made. Instead, we…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…