相关论文: Computation of the Epsilon-Subdifferential of Conv…

This paper deals with nonsmooth convex optimization problems in Euclidean spaces. We identify special elements of the subdifferential of a convex function, called specular gradients. Based on this observation, we propose three numerical…

We consider the problem of exact reconstruction of univariate functions with jump discontinuities at unknown positions from their moments. These functions are assumed to satisfy an a priori unknown linear homogeneous differential equation…

This study presents a novel algorithm for identifying the set of extreme points that constitute the exact convex hull of a point set in high-dimensional Euclidean space. The proposed method iteratively solves a sequence of dynamically…

Separability of multivariate functions alleviates the difficulty in finding a minimum or maximum value of a function such that an optimal solution can be searched by solving several disjoint problems with lower dimensionalities. In most of…

This paper develops a correspondence relating convex hulls of fractional functions with those of polynomial functions over the same domain. Using this result, we develop a number of new reformulations and relaxations for fractional…

We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…

We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…

We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…

We introduce a polynomial time algorithm for optimizing the class of star-convex functions, under no restrictions except boundedness on a region about the origin, and Lebesgue measurability. The algorithm's performance is polynomial in the…

Many separable nonlinear optimization problems can be approximated by their nonlinear objective functions with piecewise linear functions. A natural question arising from applying this approach is how to break the interval of interest into…

In this paper we characterize sharp time-data tradeoffs for optimization problems used for solving linear inverse problems. We focus on the minimization of a least-squares objective subject to a constraint defined as the sub-level set of a…

We consider the problem of approximating partition functions for Ising models. We make use of recent tools in combinatorial optimization: the Sherali-Adams and Lasserre convex programming hierarchies, in combination with variational methods…

We consider spline estimates which preserve prescribed piecewise convex properties of the unknown function. A robust version of the penalized likelihood is given and shown to correspond to a variable halfwidth kernel smoother where the…

In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic…

A new directional derivative and a new subdifferential for set-valued convex functions are constructed, and a set-valued version of the so-called 'max-formula' is proven. The new concepts are used to characterize solutions of convex…

We present an improved algorithm for computing the $4$-edge-connected components of an undirected graph in linear time. The new algorithm uses only elementary data structures, and it is simple to describe and to implement in the pointer…

We consider the problem of finding a subgraph of a given graph which maximizes a given function evaluated at its degree sequence. While the problem is intractable already for convex functions, we show that it can be solved in polynomial…

Cubic and quartic non-autonomous differential equations with continuous piecewise linear coefficients are considered. The main concern is to find the maximum possible multiplicity of periodic solutions. For many classes, we show that the…

This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions…

As a powerful tool for longitudinal data analysis, the generalized estimating equations have been widely studied in the academic community. However, in large-scale settings, this approach faces pronounced computational and storage…