Related papers: A unified approach to mixed-integer optimization p…

In this paper, we tackle the resolution of chance-constrained problems reformulated via Sample Average Approximation. The resulting data-driven deterministic reformulation takes the form of a large-scale mixed-integer program cursed with…

We consider the problem of estimation of a covariance matrix for Gaussian data in a high dimensional setting. Existing approaches include maximum likelihood estimation under a pre-specified sparsity pattern, l_1-penalized loglikelihood…

In this paper, we consider mixed-integer nonsmooth constrained optimization problems whose objective/constraint functions are available only as the output of a black-box zeroth-order oracle (i.e., an oracle that does not provide derivative…

This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…

While several classes of integer linear optimization problems are known to be solvable in polynomial time, far fewer tractability results exist for integer nonlinear optimization. In this work, we narrow this gap by identifying a broad…

We consider a 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…

Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…

We define and solve classes of sparse matrix problems that arise in multilevel modeling and data analysis. The classes are indexed by the number of nested units, with two-level problems corresponding to the common situation in which data on…

In this paper, we propose two exact distributed algorithms to solve mixed integer linear programming (MILP) problems with multiple agents where data privacy is important for the agents. A key challenge is that, because of the non-convex…

Ensemble learning combines multiple classifiers in the hope of obtaining better predictive performance. Empirical studies have shown that ensemble pruning, that is, choosing an appropriate subset of the available classifiers, can lead to…

While globally optimal solutions to many convex programs can be computed efficiently in polynomial time, this is, in general, not possible for nonconvex optimization problems. Therefore, locally optimal approaches or other efficient…

We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…

Multi-objective combinatorial optimization seeks Pareto-optimal solutions over exponentially large discrete spaces, yet existing methods sacrifice generality, scalability, or theoretical guarantees. We reformulate it as an online learning…

Mean-variance portfolio optimization problems often involve separable nonconvex terms, including penalties on capital gains, integer share constraints, and minimum position and trade sizes. We propose a heuristic algorithm for such problems…

We consider the problem of controlling a Markov decision process (MDP) with a large state space, so as to minimize average cost. Since it is intractable to compete with the optimal policy for large scale problems, we pursue the more modest…

Despite the abundance of benchmark problems for optimization algorithms, there is a notable scarcity of such problems in multidisciplinary design optimization (MDO). To address this gap, we introduce a novel methodology that enables the…

In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers…

In this paper, we introduce the concept of sparse bilinear logistic regression for decision problems involving explanatory variables that are two-dimensional matrices. Such problems are common in computer vision, brain-computer interfaces,…

In this paper, we develop a simple and fast online algorithm for solving a class of binary integer linear programs (LPs) arisen in general resource allocation problem. The algorithm requires only one single pass through the input data and…

This paper presents a mixed-integer linear programming formulation for the multi-mode resource-constrained project scheduling problem with uncertain activity durations. We consider a two-stage robust optimisation approach and find solutions…