Related papers: Optimization Algorithms for Faster Computational G…
We propose faster algorithms for the following three optimization problems on $n$ collinear points, i.e., points in dimension one. The first two problems are known to be NP-hard in higher dimensions. 1- Maximizing total area of disjoint…
The Minimum Enclosing Ball (MEB) problem is one of the most fundamental problems in clustering, with applications in operations research, statistics and computational geometry. In this works, we give the first differentially private (DP)…
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…
Linear inverse problems arise in diverse engineering fields especially in signal and image reconstruction. The development of computational methods for linear inverse problems with sparsity is one of the recent trends in this field. The…
We develop simple and general techniques to obtain faster (near-linear time) static approximation algorithms, as well as efficient dynamic data structures, for four fundamental geometric optimization problems: minimum piercing set (MPS),…
There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees,…
We propose stochastic optimization algorithms that can find local minima faster than existing algorithms for nonconvex optimization problems, by exploiting the third-order smoothness to escape non-degenerate saddle points more efficiently.…
An important goal in algorithm design is determining the best running time for solving a problem (approximately). For some problems, we know the optimal running time, assuming certain conditional lower bounds. In this work, we study the…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
Optimal stopping is a fundamental class of stochastic dynamic optimization problems with numerous applications in finance and operations management. We introduce a new approach for solving computationally-demanding stochastic optimal…
In this work, we study the computational complexity of reducing the squared gradient magnitude for smooth minimax optimization problems. First, we present algorithms with accelerated $\mathcal{O}(1/k^2)$ last-iterate rates, faster than the…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such…
We consider the traveling salesman problem when the cities are points in R^d for some fixed d and distances are computed according to geometric distances, determined by some norm. We show that for any polyhedral norm, the problem of finding…
This paper presents a spatial optimization methodology that extends the Spatial Packaging of Interconnected Systems with Physical Interaction (SPI2) framework to support arbitrary, non-convex design boundaries. We introduce a smooth,…
Designing faster algorithms for solving Mixed-Integer Linear Programming (MILP) problems is highly desired across numerous practical domains, as a vast array of complex real-world challenges can be effectively modeled as MILP formulations.…
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…
We present different methods to increase the performance of Hybrid Monte Carlo simulations of the Hubbard model in two-dimensions. Our simulations concentrate on a hexagonal lattice, though can be easily generalized to other lattices. It is…
Convex optimization is a well-established research area with applications in almost all fields. Over the decades, multiple approaches have been proposed to solve convex programs. The development of interior-point methods allowed solving a…