Related papers: SnapVX: A Network-Based Convex Optimization Solver

Writing programs for heterogeneous platforms optimized for high performance is hard since this requires the code to be tuned at a low level with architecture-specific optimizations that are most times based on fundamentally differing…

Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and…

In this paper, we consider the problem of stochastic optimization, where the objective function is in terms of the expectation of a (possibly non-convex) cost function that is parametrized by a random variable. While the convergence speed…

We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial…

This paper introduces pycvxset, a new Python package to manipulate and visualize convex sets. We support polytopes and ellipsoids, and provide user-friendly methods to perform a variety of set operations. For polytopes, pycvxset supports…

In this paper, we propose a uniform semismooth Newton-based algorithmic framework called SSNCVX for solving a broad class of convex composite optimization problems. By exploiting the augmented Lagrangian duality, we reformulate the original…

We present Sketch 'n Solve, an open-source Python package that implements efficient randomized numerical linear algebra (RandNLA) techniques for solving large-scale least squares problems. While sketch-and-solve algorithms have demonstrated…

We introduce custom code generation for parametrized convex optimization problems that supports evaluating the derivative of the solution with respect to the parameters, i.e., differentiating through the optimization problem. We extend the…

Graph-based variational methods have recently shown to be highly competitive for various classification problems of high-dimensional data, but are inherently difficult to handle from an optimization perspective. This paper proposes a convex…

Support Vector Machines (SVM), a popular machine learning technique, has been applied to a wide range of domains such as science, finance, and social networks for supervised learning. Whether it is identifying high-risk patients by…

Recent work has shown how to embed differentiable optimization problems (that is, problems whose solutions can be backpropagated through) as layers within deep learning architectures. This method provides a useful inductive bias for certain…

Recently, message-passing graph neural networks (MPNNs) have shown potential for solving combinatorial and continuous optimization problems due to their ability to capture variable-constraint interactions. While existing approaches leverage…

We describe a modular rewriting system for translating optimization problems written in a domain-specific language to forms compatible with low-level solver interfaces. Translation is facilitated by reductions, which accept a category of…

In this paper, we introduce the solver ConvexFlows for the convex flow problem first defined in the authors' previous work. In this problem, we aim to optimize a concave utility function depending on the flows over a graph. However, unlike…

Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an…

This paper describes Convex, a convex optimization modeling framework in Julia. Convex translates problems from a user-friendly functional language into an abstract syntax tree describing the problem. This concise representation of the…

Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al.~2006), this is essentially the only class of…

Determining the vanishing points (VPs) in a Manhattan world, as a fundamental task in many 3D vision applications, consists of jointly inferring the line-VP association and locating each VP. Existing methods are, however, either sub-optimal…

Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…

Chance constraints are a valuable tool for the design of safe decisions in uncertain environments; they are used to model satisfaction of a constraint with a target probability. However, because of possible non-convexity and non-smoothness,…