Related papers: Optimal Methods for Unknown Piecewise Smooth Probl…
We introduce a semidefinite relaxation for optimal control of linear systems with time scaling. These problems are inherently nonconvex, since the system dynamics involves bilinear products between the discretization time step and the…
We propose novel optimal and parameter-free algorithms for computing an approximate solution with small (projected) gradient norm. Specifically, for computing an approximate solution such that the norm of its (projected) gradient does not…
We consider the problem of finding optimal piecewise constant approximations of one-dimensional signals. These approximations should consist of a specified number of segments (samples) and minimise the mean squared error to the original…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
We consider global efficiency of algorithms for minimizing a sum of a convex function and a composition of a Lipschitz convex function with a smooth map. The basic algorithm we rely on is the prox-linear method, which in each iteration…
The present work investigates the segmentation of textures by formulating it as a strongly convex optimization problem, aiming to favor piecewise constancy of fractal features (local variance and local regularity) widely used to model…
The cone of positive-semidefinite (PSD) matrices is fundamental in convex optimization, and we extend this notion to tensors, defining PSD tensors, which correspond to separable quantum states. We study the convex optimization problem over…
This work concerns the local convergence theory of Newton and quasi-Newton methods for convex-composite optimization: minimize f(x):=h(c(x)), where h is an infinite-valued proper convex function and c is C^2-smooth. We focus on the case…
We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. For this problem, lower bounds on the number of gradient computations and the number of communication…
Convex-concave min-max problems are ubiquitous in machine learning, and people usually utilize first-order methods (e.g., gradient descent ascent) to find the optimal solution. One feature which separates convex-concave min-max problems…
Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an…
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…
Infinite-horizon optimal control of constrained piecewise affine (PWA) systems has been approximately addressed by hybrid model predictive control (MPC), which, however, has computational limitations, both in offline design and online…
Given an infeasible, unbounded, or pathological convex optimization problem, a natural question to ask is: what is the smallest change we can make to the problem's parameters such that the problem becomes solvable? In this paper, we address…
In this paper, we study the fundamental open question of finding the optimal high-order algorithm for solving smooth convex minimization problems. Arjevani et al. (2019) established the lower bound $\Omega\left(\epsilon^{-2/(3p+1)}\right)$…
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
We consider feasibility and constrained optimization problems defined over smooth and/or strongly convex sets. These notions mirror their popular function counterparts but are much less explored in the first-order optimization literature.…
Suppose that $\ff \in \reals^{n}$ is a vector of $n$ error-contaminated measurements of $n$ smooth values measured at distinct and strictly ascending abscissae. The following projective technique is proposed for obtaining a vector of smooth…
This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…
This paper is concerned with a shape optimization problem governed by a non-smooth PDE, i.e., the nonlinearity in the state equation is not necessarily differentiable. We follow the functional variational approach of [40] where the set of…