Operator Splitting for a Homogeneous Embedding of the Linear Complementarity Problem

O’Donoghue, Brendan

doi:10.1137/20m1366307

Cited by 32 publications

(21 citation statements)

References 44 publications

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“…where the first step is due to completing squares. Letting ρ = 2γ for some γ ∈ (0, 1) in the inequality above gives (10), which completes the proof.…”

Section: Appendix I Proof Of Lemmamentioning

confidence: 63%

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Proportional-Integral Projected Gradient Method for Model Predictive Control

Elango

Açıkmeşe

2021

2021 American Control Conference (ACC)

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Recently there has been an increasing interest in primal-dual methods for model predictive control (MPC), which require minimizing the (augmented) Lagrangian at each iteration. We propose a novel first order primal-dual method, termed proportional-integral projected gradient method, for MPC where the underlying finite horizon optimal control problem has both state and input constraints. Instead of minimizing the (augmented) Lagrangian, each iteration of our method only computes a single projection onto the state and input constraint set. We prove that our method ensures convergence to optimal solutions at Op1{kq and Op1{k 2 q rate if the objective function is convex and, respectively, strongly convex. We demonstrate our method via a trajectory-planning example with convexified keep-out-zone constraints.

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“…where the first step is due to completing squares. Letting ρ = 2γ for some γ ∈ (0, 1) in the inequality above gives (10), which completes the proof.…”

Section: Appendix I Proof Of Lemmamentioning

confidence: 63%

“…Traditional conic optimization methods detect infeasibility by computing matrix inverse (or equivalently, solving linear equation systems), usually as a subroutine of the interiorpoint method [6] or the Douglas-Rachford-splitting method [7], [1], [8], [9], [2], [10]. Such computation is numerically expensive for large-scale problems.…”

Section: Introductionmentioning

confidence: 99%

Proportional-Integral Projected Gradient Method for Model Predictive Control

Elango

Açıkmeşe

2021

2021 American Control Conference (ACC)

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“…The semi-definite program described by Equations ( 40)-( 42) was implemented in the python-embedded modeling language cvxpy [32] and solved using the splitting conic solver [33].…”

Section: Simulation Resultsmentioning

confidence: 99%

Robust Economic MPC of the Absorption Column in Post-Combustion Carbon Capture through Zone Tracking

Decardi‐Nelson

Liu

2022

Energies

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Several studies have reported the importance of optimally operating the absorption column in a post-combustion CO2 capture (PCC) plant. It has been demonstrated in our previous work how economic model predictive control (EMPC) has a great potential to improve the operation of the PCC plant. However, the use of a general economic objective such as maximizing the absorption efficiency of the column can cause EMPC to drive the state of the system close to the constraints. This may lead to solvent overcirculation and flooding, which are undesirable. In this work, we present an EMPC with zone tracking algorithm as an effective means to address this problem. The proposed control algorithm incorporates a zone tracking objective and an economic objective to form a multi-objective optimal control problem. To ensure that the zone tracking objective is achieved in the presence of model uncertainties and time-varying flue gas flow rate, we propose a method to modify the original target zone with a control invariant set. The zone modification method combines both ellipsoidal control invariant set techniques and a back-off strategy. The use of ellipsoidal control invariant sets ensure that the method is applicable to large scale systems such as the absorption column. We present several simulation case studies that demonstrate the effectiveness and applicability of the proposed control algorithm to the absorption column in a post-combustion CO2 capture plant.

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“…Meanwhile, in the last two decades, a number of scalable SDP solvers were successfully developed. For example, the packages PENNON [62] and SDPNAL+ [103] are based on the Augmented Lagrangian method, and SCS [82] is based on the Alternating Direction of Multipliers method (ADMM). A comprehensive review of the latest advancements in the scalability of SDP solvers is given in [74].…”

Section: Sensor Network Localization Via Semidefinite Programming Rel...mentioning

confidence: 99%

“…We compare results in terms of runtime and RMSD with three well-established solvers: DSDP v5.8 [15], a generic SDP solver based on a second-order dual interior-point method, SCS (Splitting Conic Solver) version 3.1.0 [82], a generic large-scale conic solver based on ADMM, and SDPNAL+ version 1.0 [103], a large-scale SDP solver based on a semismooth Newton-CG augmented Lagrangian method. We run the same examples listed in table 3.…”

Section: Comparisonsmentioning

confidence: 99%

A gradient descent akin method for constrained optimization: algorithms and applications

Chen¹,

Bletzinger²,

Gauger³

et al. 2023

Preprint

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We present a first-order method for solving constrained optimization problems. The method is derived from our previous work [28], a modified search direction method inspired by singular value decomposition. In this work, we simplify its computational framework to a "gradient descent akin" method (GDAM), i.e., the search direction is computed using a linear combination of the negative and normalized objective and constraint gradient. We give fundamental theoretical guarantees on the global convergence of the method. This work focuses on the algorithms and applications of GDAM. We present computational algorithms that adapt common strategies for the gradient descent method. We demonstrate the potential of the method using two engineering applications, shape optimization and sensor network localization. When practically implemented, GDAM is robust and very competitive in solving the considered large and challenging optimization problems.

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Operator Splitting for a Homogeneous Embedding of the Linear Complementarity Problem

Cited by 32 publications

References 44 publications

Proportional-Integral Projected Gradient Method for Model Predictive Control

Proportional-Integral Projected Gradient Method for Model Predictive Control

Robust Economic MPC of the Absorption Column in Post-Combustion Carbon Capture through Zone Tracking

A gradient descent akin method for constrained optimization: algorithms and applications

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