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Deep neural networks (DNNs) frequently contain far more weights, represented at a higher precision, than are required for the specific task which they are trained to perform. Consequently, they can often be compressed using techniques such…
To solve ever more complex problems, Deep Neural Networks are scaled to billions of parameters, leading to huge computational costs. An effective approach to reduce computational requirements and increase efficiency is to prune unnecessary…
Combinatorial samplers are algorithmic schemes devised for the approximate- and exact-size generation of large random combinatorial structures, such as context-free words, various tree-like data structures, maps, tilings, RNA molecules.…
We introduce an output layer for neural networks that ensures satisfaction of convex constraints. Our approach, $\Pi$net, leverages operator splitting for rapid and reliable projections in the forward pass, and the implicit function theorem…
In wireless network, the optimization problems generally have complex constraints, and are usually solved via utilizing the traditional optimization methods that have high computational complexity and need to be executed repeatedly with the…
In recent years, the integration of Machine Learning (ML) models with Operation Research (OR) tools has gained popularity across diverse applications, including cancer treatment, algorithmic configuration, and chemical process optimization.…
In this paper, we propose a branch-and-bound algorithm for solving nonconvex quadratic programming problems with box constraints (BoxQP). Our approach combines existing tools, such as semidefinite programming (SDP) bounds strengthened…
The reduction of constraints to obtain minimal representations of sets is a very common problem in many engineering applications. While well-established methodologies exist for the case of linear constraints, the problem of how to detect…
The training of two-layer neural networks with nonlinear activation functions is an important non-convex optimization problem with numerous applications and promising performance in layerwise deep learning. In this paper, we develop exact…
An emerging class of trajectory optimization methods enforces collision avoidance by jointly optimizing the robot's configuration and a separating hyperplane. However, as linear separators only apply to convex sets, these methods require…
We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…
When computing bounds, spatial branch-and-bound algorithms often linearly outer approximate convex relaxations for non-convex expressions in order to capitalize on the efficiency and robustness of linear programming solvers. Considering…
We study the question of whether parallelization in the exploration of the feasible set can be used to speed up convex optimization, in the local oracle model of computation. We show that the answer is negative for both deterministic and…
This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…
We present a neural network approach for fast evaluation of parameter-dependent polyconvex envelopes, which are crucial in computational mechanics. Our method uses a neural network architecture that inherently encodes polyconvexity in the…
Automatic performance tuning, or auto-tuning, accelerates high-performance codes by exploring vast spaces of code variants. However, due to the large number of possible combinations and complex constraints, constructing these search spaces…
The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can convert this problem into a nested sequence of…
This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…
In this paper we propose a set of guidelines to select a solver for the solution of nonlinear programming problems. With this in mind, we present a comparison of the convergence performances of commonly used solvers for both unconstrained…
This paper addresses a class of (non-)convex optimization problems subject to general convex constraints, which pose significant challenges for traditional methods due to their inherent non-convexity and diversity. Conventional convex…