Related papers: Compiling Stochastic Constraint Programs to And-Or…

The minimum sum-of-squares clustering (MSSC), or k-means type clustering, has been recently extended to exploit prior knowledge on the cardinality of each cluster. Such knowledge is used to increase performance as well as solution quality.…

Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…

Random sampling of graph partitions under constraints has become a popular tool for evaluating legislative redistricting plans. Analysts detect partisan gerrymandering by comparing a proposed redistricting plan with an ensemble of sampled…

We present an algorithm for recovering planted solutions in two well-known models, the stochastic block model and planted constraint satisfaction problems, via a common generalization in terms of random bipartite graphs. Our algorithm…

Motion planning for autonomous driving must account for multi-modal uncertainty in both the intentions and trajectories of surrounding vehicles. Handling uncertainty in a worst-case manner guarantees robustness but often leads to excessive…

In this paper, we introduce a significant extension, called scenario with certificates (SwC), of the so-called scenario approach for uncertain optimization problems. This extension is motivated by the observation that in many control…

The Container Relocation Problem (CRP) is concerned with finding a sequence of moves of containers that minimizes the number of relocations needed to retrieve all containers, while respecting a given order of retrieval. However, the…

Stochastic programming can be applied to consider uncertainties in energy system optimization models for capacity expansion planning. However, these models become increasingly large and time-consuming to solve, even without considering…

Policy optimization is among the most popular and successful reinforcement learning algorithms, and there is increasing interest in understanding its theoretical guarantees. In this work, we initiate the study of policy optimization for the…

In reinforcement learning, the state of the real world is often represented by feature vectors. However, not all of the features may be pertinent for solving the current task. We propose Feature Selection Explore and Exploit (FS-EE), an…

This paper explores the use of Answer Set Programming (ASP) in solving Distributed Constraint Optimization Problems (DCOPs). The paper provides the following novel contributions: (1) It shows how one can formulate DCOPs as logic programs;…

A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…

We propose a novel distribution-free scheme to solve optimization problems where the goal is to minimize the expected value of a cost function subject to probabilistic constraints. Unlike standard sampling-based methods, our idea consists…

The Angular Constrained Minimum Spanning Tree Problem ($\alpha$-MSTP) is defined in terms of a complete undirected graph $G=(V,E)$ and an angle $\alpha \in (0,2\pi]$. Vertices of $G$ define points in the Euclidean plane while edges, the…

Modeling decision-dependent scenario probabilities in stochastic programs is difficult and typically leads to large and highly non-linear MINLPs that are very difficult to solve. In this paper, we develop a new approach to obtain a compact…

Stochastic dual dynamic programming (SDDP) is a state-of-the-art method for solving multi-stage stochastic optimization, widely used for modeling real-world process optimization tasks. Unfortunately, SDDP has a worst-case complexity that…

It is well-known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max-cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show…

Semidefinite programs (SDPs) often arise in relaxations of some NP-hard problems, and if the solution of the SDP obeys certain rank constraints, the relaxation will be tight. Decomposition methods based on chordal sparsity have already been…

We investigate a class of chance-constrained combinatorial optimization problems. Given a pre-specified risk level $\epsilon \in [0,1]$, the chance-constrained program aims to find the minimum cost selection of a vector of binary decisions…

The factor graph of an instance of a symmetric constraint satisfaction problem on n Boolean variables and m constraints (CSPs such as k-SAT, k-AND, k-LIN) is a bipartite graph describing which variables appear in which constraints. The…