Related papers: A seven-point algorithm for piecewise smooth univa…
A sequential quadratic optimization algorithm is proposed for solving smooth nonlinear equality constrained optimization problems in which the objective function is defined by an expectation of a stochastic function. The algorithmic…
We propose a very simple preprocessing algorithm for semidefinite programming. Our algorithm inspects the constraints of the problem, deletes redundant rows and columns in the constraints, and reduces the size of the variable matrix. It…
In this paper, we propose a unified energy minimization model for the segmentation of non-smooth image structures. The energy of piecewise linear patch reconstruction is considered as an objective measure of the quality of the segmentation…
The (unweighted) point-separation problem asks, given a pair of points $s$ and $t$ in the plane, and a set of candidate geometric objects, for the minimum-size subset of objects whose union blocks all paths from $s$ to $t$. Recent work has…
A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a…
Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We…
The idea of partial smoothness in optimization blends certain smooth and nonsmooth properties of feasible regions and objective functions. As a consequence, the standard first-order conditions guarantee that diverse iterative algorithms…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
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…
In this paper we propose a computationally efficient algorithm for on-line variable selection in multivariate regression problems involving high dimensional data streams. The algorithm recursively extracts all the latent factors of a…
We consider a family of algorithms that successively sample and minimize simple stochastic models of the objective function. We show that under reasonable conditions on approximation quality and regularity of the models, any such algorithm…
We consider the problem of finding critical points of functions that are non-convex and non-smooth. Studying a fairly broad class of such problems, we analyze the behavior of three gradient-based methods (gradient descent, proximal update,…
In a recent paper, Bubeck, Lee, and Singh introduced a new first order method for minimizing smooth strongly convex functions. Their geometric descent algorithm, largely inspired by the ellipsoid method, enjoys the optimal linear rate of…
We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary location, and levels. It works for any noise and segment level prior, e.g. Cauchy which can handle outliers.…
A descent algorithm, "Quasi-Quadratic Minimization with Memory" (QQMM), is proposed for unconstrained minimization of the sum, $F$, of a non-negative convex function, $V$, and a quadratic form. Such problems come up in regularized…
Several optimization schemes have been known for convex optimization problems. However, numerical algorithms for solving nonconvex optimization problems are still underdeveloped. A progress to go beyond convexity was made by considering the…
The paper considers the problem of constructing program control for an object described by a system with a quasidifferentiable right-hand side. The control aim is to bring the system from a given initial position to a given final state in…
Sparse inverse covariance selection is a fundamental problem for analyzing dependencies in high dimensional data. However, such a problem is difficult to solve since it is NP-hard. Existing solutions are primarily based on convex…
We consider the problem of computing the minimum of a polynomial function g on a basic closed semialgebraic set E in R^n. We present a probabilistic symbolic algorithm to find a finite set of sample points of the subset E^{min} of E where…
In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regularization techniques are used within…