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This paper presents a novel learning-based approach to construct a surrogate problem that approximates a given parametric nonconvex optimization problem. The surrogate function is designed to be the minimum of a finite set of functions,…
We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…
Asynchronous distributed algorithms are a popular way to reduce synchronization costs in large-scale optimization, and in particular for neural network training. However, for nonsmooth and nonconvex objectives, few convergence guarantees…
Boolean quadratic optimization problems occur in a number of applications. Their mixed integer-continuous nature is challenging, since it is inherently NP-hard. For this motivation, semidefinite programming relaxations (SDR's) are proposed…
We explore a reinforcement learning strategy to automate and accelerate h/p-multigrid methods in high-order solvers. Multigrid methods are very efficient but require fine-tuning of numerical parameters, such as the number of smoothing…
The repeated solution of large-scale optimization problems arises frequently in process systems engineering tasks. Decomposition-based solution methods have been widely used to reduce the corresponding computational time, yet their…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
This paper extends algorithms that remove the fixed point bias of decentralized gradient descent to solve the more general problem of distributed optimization over subspace constraints. Leveraging the integral quadratic constraint…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…
Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
A general method for accelerating fixed point schemes for problems related to partial differential equations is presented in this article. The speedup is obtained by training a reduced-order model on-the-fly, removing the need to do an…
We introduce the \emph{submodular objectives chasing problem}, which generalizes many natural and previously-studied problems: a sequence of constrained submodular maximization problems is revealed over time, with both the objective and…
Optimization problems with nonlinear cost functions and combinatorial constraints appear in many real-world applications but remain challenging to solve efficiently compared to their linear counterparts. To bridge this gap, we propose…
We consider joint optimization and learning problems arising in real-time decision systems. While most existing work focuses primarily on convex, revenue-based objectives, we extend this line of research to multi-objective formulations. In…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
Offline optimization is an emerging problem in many experimental engineering domains including protein, drug or aircraft design, where online experimentation to collect evaluation data is too expensive or dangerous. To avoid that, one has…
We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…
We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…