Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding

By Brendan O'Donoghue, Eric King-Wah Chu, Neal Parikh, Stephen P. Boyd. 2013

844 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

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Citations in the corpus

Solving Mixed Integer Programs Using Neural Networks (2020, methodology): “…to scale to a large number of candidate variables at a reasonable cost we wrote our own batch LP solver using the alternating directions method of multipliers (ADMM) (Boyd et al. 2011), based on the Splitting Conic Solver (SCS) algorithm for cone programs (O’Donoghue et al. 2016, O’Donoghue 2020).”
Generative modeling for protein structures (2018, background): “We found that indirect solvers like SCS were not able to handle problems with n > 115 (Figure S1b) [33, 34].”
A Rewriting System for Convex Optimization Problems (2017, background): “For example, ﬁrst-order solvers like SCS scale to larger problems than interior-point methods like ECOS, though the latter typically provide more accurate solutions than do the former.”
Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulator (2018, methodology): “For our experiments, we used the SCS solver [19] via CVXPY [9].”
Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data (2017, methodology): “For smaller covariances, this semidefinite programming problem can be solved using standard interior point methods [6, 36].”
Linear convergence of first order methods for non-strongly convex optimization (2015, background): “Therefore,aprimal-dual solution of (68)–(69) can be found by solving the following convex feasibility problem: ﬁnd ( u , v, s ) such that authors in [21] proposed solving conic optimization problems given in the previous form using ADMM.”
PowerModels.J1: An Open-Source Framework for Exploring Power Flow Formulations (2017, methodology): “This abstraction layer is highly valuable for two reasons: (1) Within the same problem class (e.g. linear programs), it is easy to explore a number of different solver technologies (e.g. CLP, GLPK, CPLEX, Gurobi); (2) When modifications in the mathematical specification changes the problem class (e.”
CVXPY: A Python-Embedded Modeling Language for Convex Optimization (2016, methodology): “CVXPY interfaces with the open-source cone solvers CVX-OPT (Andersen et al., 2015), ECOS (Domahidi et al., 2013), and SCS (O’Donoghue et al., 2016), which are implemented in combinations of Python and C.”
Perspective Functions: Proximal Calculus and Applications in High-Dimensional Statistics (2016, methodology): “We use SCS in indirect mode [22] to solve the SOCP formulation of the TREX subproblem [3] with convergence tolerance 10−4.”
Operator Splitting for a Homogeneous Embedding of the Linear Complementarity Problem (2020, methodology): “For the special case of QCPs with P = 0 the problem reduces to a linear cone program of the form that the original SCS algorithm [56] was developed to tackle.”
Fast online deconvolution of calcium imaging data (2016, methodology): “We compared the run time of our algorithm to a variety of state of the art convex solvers that can all be conveniently called from the convex optimization toolbox CVXPY [38]: embedded conic solver (ECOS, [39]), MOSEK [40], splitting conic solver (SCS, [41]) and GUROBI [42].”
AOWS: Adaptive and Optimal Network Width Search With Latency Constraints (2020, methodology): “Rather than enforcing these inequalities in a hard way, we found it best to use a soft prior, which translates into where the weighting parameter λ is set using a validation set; this minimization can be solved efﬁciently using a second-order cone program solver [4, 17].”
Stochastic matrix games with bandit feedback (2020, background): “The optimization problem in algorithm 3 is convex and can be expressed as an exponential cone program, for which efﬁcient algorithms exist [27, 38, 15].”
Edge Artificial Intelligence for 6G: Vision, Enabling Technologies, and Applications (2021, methodology): “This is achieved by automatically transforming the original problem instances into standard conic programming forms, followed by calling the advanced off-the-shelf conic solvers, e.g., MOSEK [296] and SCS [113].”