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Molecular dynamics is one of the most commonly used approaches for studying the dynamics and statistical distributions of many physical, chemical, and biological systems using atomistic or coarse-grained models. It is often the case,…
Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…
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…
Bilevel optimization has been widely used in decision-making process. However, there still lacks an efficient algorithm to determine an optimal solution of a bilevel optimization problem, especially for a large-size problem. To bridge the…
In this paper, we consider non-convex multi-block bilevel optimization (MBBO) problems, which involve $m\gg 1$ lower level problems and have important applications in machine learning. Designing a stochastic gradient and controlling its…
Two-stage stochastic programming is a popular framework for optimization under uncertainty, where decision variables are split between first-stage decisions, and second-stage (or recourse) decisions, with the latter being adjusted after…
This paper studies the dynamic programming principle using the measurable selection method for stochastic control of continuous processes. The novelty of this work is to incorporate intermediate expectation constraints on the canonical…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
In dual decomposition, the dual to an optimization problem with a specific structure is solved in distributed fashion using (sub)gradient and recently also fast gradient methods. The traditional dual decomposition suffers from two main…
Symbolic regression that aims to detect underlying data-driven models has become increasingly important for industrial data analysis. For most existing algorithms such as genetic programming (GP), the convergence speed might be too slow for…
This article presents an overview of a research study of a crucial optimization problem in the Computer Science/Operations research field: The Job-shop Scheduling Problem (JSP). The JSP is a challenging task in which a set of operations…
In this paper, we analyze dynamic programming as a novel approach to solve the problem of maximizing the profits of a bank. The mathematical model of the problem and the description of a bank's work is described in this paper. The problem…
We consider an optimal stopping problem where a constraint is placed on the distribution of the stopping time. Reformulating the problem in terms of so-called measure-valued martingales allows us to transform the marginal constraint into an…
This paper presents two new approaches to decomposing and solving large Markov decision problems (MDPs), a partial decoupling method and a complete decoupling method. In these approaches, a large, stochastic decision problem is divided into…
Stochastic programming provides a natural framework for modeling sequential optimization problems under uncertainty; however, the efficient solution of large-scale multistage stochastic programs remains a challenge, especially in the…
A standard assumption in multistage stochastic programming is that decisions are made after observing the uncertainty from the prior stage. The resulting solutions can be difficult to implement in practice, as they leave practitioners…
In this paper, we propose a mathematical formulation for the management of an oil production network as a multistage optimization problem. The reservoir is modeled as a controlled dynamical system by using material balance equations. We use…
In this paper, we study multi-block min-max bilevel optimization problems, where the upper level is non-convex strongly-concave minimax objective and the lower level is a strongly convex objective, and there are multiple blocks of dual…
Optimizing decision problems under uncertainty can be done using a variety of solution methods. Soft computing and heuristic approaches tend to be powerful for solving such problems. In this overview article, we survey Evolutionary…
Finite-dimensional dissipative dynamical systems with multiple time-scales are obtained when modeling chemical reaction kinetics with ordinary differential equations. Such stiff systems are computationally hard to solve and therefore,…