A Quasi-Newton Algorithm for Optimal Discretization of Markov Processes

In stochastic programming and stochastic-dynamic programming discretization of random model parameters is often unavoidable. We propose a quasi-Newton learning algorithm to discretize multi-dimensional, continuous discrete-time Markov processes to scenario lattices by minimizing the Wasserstein distance between the unconditional distributions of process and lattice. Scenario lattices enable accurate discretization of the conditional distributions of Markov processes … Read more

Mixed-Integer Quadratic Optimization and Iterative Clustering Techniques for Semi-Supervised Support Vector Machines

Among the most famous algorithms for solving classification problems are support vector machines (SVMs), which find a separating hyperplane for a set of labeled data points. In some applications, however, labels are only available for a subset of points. Furthermore, this subset can be non-representative, e.g., due to self-selection in a survey. Semi-supervised SVMs tackle … Read more

Machine Learning for K-adaptability in Two-stage Robust Optimization

Two-stage robust optimization problems constitute one of the hardest optimization problem classes.One of the solution approaches to this class of problems is K-adaptability. This approach simultaneously seeks the best partitioning of the uncertainty set of scenarios into K subsets, and optimizesdecisions corresponding to each of these subsets. In general case, it is solved using the … Read more

Statistical performance of subgradient step-size update rules in Lagrangian relaxations of chance-constrained optimization models

Lagrangian relaxation schemes, coupled with a subgradient procedure, are frequently employed to solve chance-constrained optimization models. The subgradient procedure typically relies on a step-size update rule. Although there is extensive research on the properties of these step-size update rules, there is little consensus on which rules are most suited in practice. This is especially so … Read more

Time-series aggregation for the optimization of energy systems: goals, challenges, approaches, and opportunities

The rising significance of renewable energy increases the importance of representing time-varying input data in energy system optimization studies. Time-series aggregation, which reduces temporal model complexity, has emerged in recent years to address this challenge. We provide a comprehensive review of time-series aggregation for the optimization of energy systems. We show where time series affect … Read more

On the Cluster-aware Supervised Learning (CluSL): Frameworks, Convergent Algorithms, and Applications

This paper proposes a cluster-aware supervised learning (CluSL) framework, which integrates the clustering analysis with supervised learning (SL). The objective of CluSL is to simultaneously find the best clusters of the data points and minimize the sum of loss functions within each cluster. This framework has many potential applications in healthcare, operations management, manufacturing, and … Read more

Clustering methods to find representative periods for the optimization of energy systems: an initial framework and comparison

Modeling time-varying operations in complex energy systems optimization problems is often computationally intractable, and time-series input data are thus often aggregated to representative periods. In this work, we introduce a framework for using clustering methods for this purpose, and we compare both conventionally-used methods (k-means, k-medoids, and hierarchical clustering), and shape-based clustering methods (dynamic time … Read more

Clustering and Multifacility Location with Constraints via Distance Function Penalty Method and DC Programming

This paper is a continuation of our effort in using mathematical optimization involving DC programming in clustering and multifacility location. We study a penalty method based on distance functions and apply it particularly to a number of problems in clustering and multifacility location in which the centers to be found must lie in some given … Read more

Divisive heuristic for modularity density maximization

In this paper we consider a particular method of clustering for graphs, namely the modularity density maximization. We propose a hierarchical divisive heuristic which works by splitting recursively a cluster into two new clusters by maximizing the modularity density, and we derive four reformulations for the mathematical programming model used to obtain the optimal splitting. … Read more