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Given a first-order autonomous algebraic ordinary differential equation, we present a method for computing formal power series solutions by means of places. We provide an algorithm for computing a full characterization of possible initial…
We develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial differential equations (PDEs). The PDE is first written in…
We introduce the \emph{submodular objectives chasing problem}, which generalizes many natural and previously-studied problems: a sequence of constrained submodular maximization problems is revealed over time, with both the objective and…
Many computer vision and image processing problems can be posed as solving partial differential equations (PDEs). However, designing PDE system usually requires high mathematical skills and good insight into the problems. In this paper, we…
This article investigates the approximation quality achievable for biobjective minimization problems with respect to the Pareto cone by solutions that are (approximately) optimal with respect to larger ordering cones. When simultaneously…
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…
A depth map can be represented by a set of learned bases and can be efficiently solved in a closed form solution. However, one issue with this method is that it may create artifacts when colour boundaries are inconsistent with depth…
Motivated by a growing list of nontraditional statistical estimation problems of the piecewise kind, this paper provides a survey of known results supplemented with new results for the class of piecewise linear-quadratic programs. These are…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
We study a class of linear ordinary differential equations (ODE)s with distributional coefficients. These equations are defined using an {\it intrinsic} multiplicative product of Schwartz distributions which is an extension of the…
An astonishing fact was established by Lee A. Rubel (1981): there exists a fixed non-trivial fourth-order polynomial differential algebraic equation (DAE) such that for any positive continuous function $\varphi$ on the reals, and for any…
Many practical optimization problems lack strong convexity. Fortunately, recent studies have revealed that first-order algorithms also enjoy linear convergences under various weaker regularity conditions. While the relationship among…
In this article we study optimal control problems for systems that are affine in one part of the control variable. Finitely many equality and inequality constraints on the initial and final values of the state are considered. We investigate…
Various first order approaches have been proposed in the literature to solve Linear Programming (LP) problems, recently leading to practically efficient solvers for large-scale LPs. From a theoretical perspective, linear convergence rates…
In many recent applications when new materials and technologies are developed it is important to describe and simulate new nonlinear and nonlocal diffusion transport processes. A general class of such models deals with nonlocal fractional…
We consider the ideal orientation problem in planar graphs. In this problem, we are given an undirected graph $G$ with positive edge lengths and $k$ pairs of distinct vertices $(s_1, t_1), \dots, (s_k, t_k)$ called terminals, and we want to…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
We consider the problem of computing an equilibrium in a class of \textit{nonlinear generalized Nash equilibrium problems (NGNEPs)} in which the strategy sets for each player are defined by equality and inequality constraints that may…
This paper presents a canonical dual method for solving a quadratic discrete value selection problem subjected to inequality constraints. The problem is first transformed into a problem with quadratic objective and 0-1 integer variables.…
The paper studies the First Order BSPDEs (Backward Stochastic Partial Differential Equations) suggested earlier for a case of multidimensional state domain with a boundary. These equations represent analogs of Hamilton-Jacobi-Bellman…