Related papers: Convergence of Successive Linear Programming Algor…
Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…
Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements. Through the lens of matrix and tensor…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
In this paper, we present convergence guarantees for a modified trust-region method designed for minimizing objective functions whose value and gradient and Hessian estimates are computed with noise. These estimates are produced by generic…
A trust-region algorithm is presented for finding approximate minimizers of smooth unconstrained functions whose values and derivatives are subject to random noise. It is shown that, under suitable probabilistic assumptions, the new method…
Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…
Although it is relatively easy to apply, the gradient method often displays a disappointingly slow rate of convergence. Its convergence is specially based on the structure of the matrix of the algebraic linear system, and on the choice of…
We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…
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.…
Multi-objective verification problems of parametric Markov decision processes under optimality criteria can be naturally expressed as nonlinear programs. We observe that many of these computationally demanding problems belong to the…
In this paper, we propose an improved numerical algorithm for solving minimax problems based on nonsmooth optimization, quadratic programming and iterative process. We also provide a rigorous proof of convergence for our algorithm under…
We consider non-smooth saddle point optimization problems. To solve these problems, we propose a zeroth-order method under bounded or Lipschitz continuous noise, possible adversarial. In contrast to the state-of-the-art algorithms, our…
We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…
In machine learning, stochastic gradient descent (SGD) is widely deployed to train models using highly non-convex objectives with equally complex noise models. Unfortunately, SGD theory often makes restrictive assumptions that fail to…
This work studies minimization problems with zero-order noisy oracle information under the assumption that the objective function is highly smooth and possibly satisfies additional properties. We consider two kinds of zero-order projected…
The nonlinear optimization problem with linear constraints has many applications in engineering fields such as the visual-inertial navigation and localization of an unmanned aerial vehicle maintaining the horizontal flight. In order to…
We investigate the convergence properties of a class of iterative algorithms designed to minimize a potentially non-smooth and noisy objective function, which may be algebraically intractable and whose values may be obtained as the output…
This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…
We investigate a trust-region algorithm to solve a nonconvex optimization problem with $L^p$-regularization for $p\in(0,1)$. The algorithm relies on descent properties of a so-called generalized Cauchy point that can be obtained efficiently…
We explore reinforcement learning methods for finding the optimal policy in the linear quadratic regulator (LQR) problem. In particular, we consider the convergence of policy gradient methods in the setting of known and unknown parameters.…