In this paper, we propose a variant of the reduced Jacobian method (RJM) introduced by El Maghri and Elboulqe in [JOTA, 179 (2018) 917–943] for multicriteria optimization under linear constraints. Motivation is that, contrarily to RJM which has only global convergence to Pareto KKT-stationary points in the classical sense of accumulation points, this new variant … Read more
We propose a new robust actionable prescriptive analytics framework that leverages past data and side information to minimize a risk-based objective function under distributional ambiguity. Our framework aims to find a policy that directly transforms the side information into implementable decisions. Specifically, we focus on developing actionable response policies that offer the benefits of interpretability … Read more
Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing methods, especially Quantum Interior Point Methods (QIPMs), to solve convex optimization problems, such as Linear Optimization, Semidefinite Optimization, and Second-order Cone Optimization problems. Most of them have … Read more
\(\) While useful probability bounds for \(n\) pairwise independent Bernoulli random variables adding up to at least an integer \(k\) have been proposed in the literature, none of these bounds are tight in general. In this paper, we provide several results in this direction. Firstly, when \(k = 1\), the tightest upper bound on the … Read more
We consider the widely-studied class of production-inventory problems with box uncertainty sets from the seminal work of Ben-Tal et al. (2004) on linear decision rules in robust optimization. We prove that there always exists an optimal linear decision rule for this class of problems in which the number of nonzero parameters in the linear decision … Read more
Currently, the simplex method and the interior point method are indisputably the most popular algorithms for solving linear programs, LPs. Unlike general conic programs, LPs with a finite optimal value do not require strict feasibility in order to establish strong duality. Hence strict feasibility is seldom a concern, even though strict feasibility is equivalent to … Read more
We study the computational complexity of the optimal transport problem that evaluates the Wasserstein distance between the distributions of two K-dimensional discrete random vectors. The best known algorithms for this problem run in polynomial time in the maximum of the number of atoms of the two distributions. However, if the components of either random vector … Read more
We consider the NP-hard problem of approximating a tensor with binary entries by a rank-one tensor, referred to as rank-one Boolean tensor factorization problem. We formulate this problem, in an extended space of variables, as the problem of minimizing a linear function over a highly structured multilinear set. Leveraging on our prior results regarding the … Read more
Intensity modulated radiation therapy (IMRT) is one of radiation therapies for cancers, and it is considered to be effective for complicated shapes of tumors, since dose distributions from each irradiation can be modulated arbitrary. Fluence map optimization (FMO), which optimizes beam intensities with given beam angles, is often formulated as an optimization problem with dose … Read more
Applying an interior-point method to the central-path conditions is a widely used approach for solving quadratic programs. Reformulating these conditions in the log-domain is a natural variation on this approach that to our knowledge is previously unstudied. In this paper, we analyze log-domain interior-point methods and prove their polynomial-time convergence. We also prove that they … Read more