Related papers: A review of the Statistical Mechanics approach to …
Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…
Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…
Stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems. We give numerical and approximate analytical descriptions of the dynamics of such algorithms applied to random…
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…
Statistical static timing analysis (SSTA) is studied from the point of view of mathematical optimization. We present two formulations of the problem of finding the critical path delay distribution that were not known before: (i) a…
Boolean satisfiability [1] (k-SAT) is one of the most studied optimization problems, as an efficient (that is, polynomial-time) solution to k-SAT (for $k\geq 3$) implies efficient solutions to a large number of hard optimization problems…
It is proposed to apply modern methods of nonlinear nonequilibrium statistical mechanics to develop software algorithms that will optimally respond to targets within short response times with minimal computer resources. This Statistical…
We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…
Optimization problems such as the NP-complete 3-SAT provide an important benchmark for the difficult task of finding ground-states in strongly correlated many-body systems with rugged energy landscapes. The study of random 3-SAT problems as…
Min-max optimization problems, also known as saddle point problems, have attracted significant attention due to their applications in various fields, such as fair beamforming, generative adversarial networks (GANs), and adversarial…
In computational science workflows, it is often the case that 1) objective functions for optimization involve multiple simulation outputs, and 2) those simulations can be performed (at least partially) in parallel. In this work, we…
Optimization problems involving sequential decisions in a stochastic environment were studied in Stochastic Programming (SP), Stochastic Optimal Control (SOC) and Markov Decision Processes (MDP). In this paper we mainly concentrate on SP…
Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…
The treatment of the number-theoretical problem of integer partitions within the approach of statistical mechanics is discussed. Historical overview is given and known asymptotic results for linear and plane partitions are reproduced. From…
Many key problems in machine learning and data science are routinely modeled as optimization problems and solved via optimization algorithms. With the increase of the volume of data and the size and complexity of the statistical models used…
Simulation Optimization (SO) refers to the optimization of an objective function subject to constraints, both of which can be evaluated through a stochastic simulation. To address specific features of a particular simulation---discrete or…
Choosing control inputs randomly can result in a reduced expected cost in optimal control problems with stochastic constraints, such as stochastic model predictive control (SMPC). We consider a controller with initial randomization, meaning…
Focusing on the optimization version of the random K-satisfiability problem, the MAX-K-SAT problem, we study the performance of the finite energy version of the Survey Propagation (SP) algorithm. We show that a simple (linear time)…
In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…
In terms of the concepts of state and state transition, a new heuristic random search algorithm named state transition algorithm is proposed. For continuous function optimization problems, four special transformation operators called…