Related papers: Parallel Optimization of Polynomials for Large-sca…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
Repair mechanisms are important within resilient systems to maintain the system in an operational state after an error occurred. Usually, constraints on the repair mechanisms are imposed, e.g., concerning the time or resources required…
Problems from graph drawing, spectral clustering, network flow and graph partitioning can all be expressed in terms of graph Laplacian matrices. There are a variety of practical approaches to solving these problems in serial. However, as…
We consider learning problems over training sets in which both, the number of training examples and the dimension of the feature vectors, are large. To solve these problems we propose the random parallel stochastic algorithm (RAPSA). We…
We consider a parallel system of $m$ identical machines prone to unpredictable crashes and restarts, trying to cope with the continuous arrival of tasks to be executed. Tasks have different computational requirements (i.e., processing time…
In this paper we consider discrete time stochastic optimal control problems over infinite and finite time horizons. We show that for a large class of such problems the Taylor polynomials of the solutions to the associated Dynamic…
Parallelization is a popular strategy for improving the performance of iterative algorithms. Optimization methods are no exception: design of efficient parallel optimization methods and tight analysis of their theoretical properties are…
Many practical applications require solving an optimization over large and high-dimensional data sets, which makes these problems hard to solve and prohibitively time consuming. In this paper, we propose a parallel distributed algorithm…
Joint channel and rate allocation with power minimization in orthogonal frequency-division multiple access (OFDMA) has attracted extensive attention. Most of the research has dealt with the development of sub-optimal but low-complexity…
Deep learning is a popular machine learning technique and has been applied to many real-world problems. However, training a deep neural network is very time-consuming, especially on big data. It has become difficult for a single machine to…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
Stable matching theory is the foundation of centralized clearinghouses worldwide, from school choice programs to medical residency allocations. However, incorporating complex distributional goals-such as multi-dimensional diversity quotas…
In distributed stochastic optimization, where parallel and asynchronous methods are employed, we establish optimal time complexities under virtually any computation behavior of workers/devices/CPUs/GPUs, capturing potential disconnections…
Self-adjusting computation is an approach for automatically producing dynamic algorithms from static ones. The approach works by tracking control and data dependencies, and propagating changes through the dependencies when making an update.…
Stochastic computer simulations enable users to gain new insights into complex physical systems. Optimization is a common problem in this context: users seek to find model inputs that maximize the expected value of an objective function.…
This paper presents a new method for synthesizing stochastic control Lyapunov functions for a class of nonlinear stochastic control systems. The technique relies on a transformation of the classical nonlinear Hamilton-Jacobi-Bellman partial…
Despite the notable success of deep neural networks (DNNs) in solving complex tasks, the training process still remains considerable challenges. A primary obstacle is the substantial time required for training, particularly as high…
Discrete time stochastic optimal control problems and Markov decision processes (MDPs), respectively, serve as fundamental models for problems that involve sequential decision making under uncertainty and as such constitute the theoretical…
This thesis addresses the question of stability of systems defined by differential equations which contain nonlinearity and delay. In particular, we analyze the stability of a well-known delayed nonlinear implementation of a certain…