Related papers: Efficient Second-Order Shape-Constrained Function …
Optimization in engineering requires appropriate models. In this article, a regression method for enhancing the predictive power of a model by exploiting expert knowledge in the form of shape constraints, or more specifically, monotonicity…
In the simultaneous Max-Cut problem, we are given $k$ weighted graphs on the same set of $n$ vertices, and the goal is to find a cut of the vertex set so that the minimum, over the $k$ graphs, of the cut value is as large as possible.…
We consider the precedence-constrained scheduling problem to minimize the total weighted completion time. For a single machine several $2$-approximation algorithms are known, which are based on linear programming and network flows. We show…
We study first-order optimization algorithms under the constraint that the descent direction is quantized using a pre-specified budget of $R$-bits per dimension, where $R \in (0 ,\infty)$. We propose computationally efficient optimization…
We consider the problem of maximizing a monotone nondecreasing set function under multiple constraints, where the constraints are also characterized by monotone nondecreasing set functions. We propose two greedy algorithms to solve the…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…
In this paper, we propose first-order feasible methods for difference-of-convex (DC) programs with smooth inequality and simple geometric constraints. Our strategy for maintaining feasibility of the iterates is based on a "retraction" idea…
In this work, we develop analysis and algorithms for a class of (stochastic) bilevel optimization problems whose lower-level (LL) problem is strongly convex and linearly constrained. Most existing approaches for solving such problems rely…
In this paper, we study stochastic non-convex optimization with non-convex random functions. Recent studies on non-convex optimization revolve around establishing second-order convergence, i.e., converging to a nearly second-order optimal…
Change-point problems have appeared in a great many applications for example cancer genetics, econometrics and climate change. Modern multiscale type segmentation methods are considered to be a statistically efficient approach for multiple…
We investigate the addition of constraints on the function image and its derivatives for the incorporation of prior knowledge in symbolic regression. The approach is called shape-constrained symbolic regression and allows us to enforce e.g.…
The task of approximating points with circular arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. However, the development of algorithms that perform a significant amount of…
Many problems are NP-hard and, unless P = NP, do not admit polynomial-time exact algorithms. The fastest known exact algorithms exactly usually take time exponential in the input size. Much research effort has gone into obtaining faster…
Optimizing non-convex functions is of primary importance in the vast majority of machine learning algorithms. Even though many gradient descent based algorithms have been studied, successive convex approximation based algorithms have been…
Rapid advances in data collection and processing capabilities have allowed for the use of increasingly complex models that give rise to nonconvex optimization problems. These formulations, however, can be arbitrarily difficult to solve in…
We study fundamental limits of first-order stochastic optimization in a range of nonconvex settings, including L-smooth functions satisfying Quasar-Convexity (QC), Quadratic Growth (QG), and Restricted Secant Inequalities (RSI). While the…
We consider the problem of minimal correction of the training set to make it consistent with monotonic constraints. This problem arises during analysis of data sets via techniques that require monotone data. We show that this problem is…
In this paper, we propose two simple yet efficient computational algorithms to obtain approximate optimal designs for multi-dimensional linear regression on a large variety of design spaces. We focus on the two commonly used optimal…
We study dynamic $(1-\epsilon)$-approximate rounding of fractional matchings -- a key ingredient in numerous breakthroughs in the dynamic graph algorithms literature. Our first contribution is a surprisingly simple deterministic rounding…
We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first…