Convergence of the Surrogate Lagrangian Relaxation Method

Bragin, Mikhail A.; Luh, Peter B.; Yan, J.H.; Yu, Nanpeng; Stern, Gary A.

doi:10.1007/s10957-014-0561-3

Cited by 138 publications

(140 citation statements)

References 30 publications

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“…Breakthroughs for the decomposition and coordination method were made in [16]. Based on surrogate subgradients, SLR that has been successfully used for a mixed-integer linear problem in [17] is used.…”

Section: Solution Methodologymentioning

confidence: 99%

“…Lower and upper bounds for the water mass flow rate of the primary pump are shown as: T T T T T T T T T Similarly, power consumption of a condenser pump is: (16) where P cp,nom is the nominal power consumption, cpw,nom is the nominal water mass flow rate and cpw is the condenser water mass flow rate of the condenser pump.…”

Section: Constraints Of Primary Pumpsmentioning

confidence: 99%

“…The updated multiplies are used for the next iteration until the dual function is maximized. Multipliers are updated as follows [16]:…”

Section: Solving the Dual Problemmentioning

confidence: 99%

See 2 more Smart Citations

A decomposition and coordination-based method for chiller plant optimization

Zhang

Luh

Fan³

et al. 2015

2015 International Conference on Complex Systems Engineering (ICCSE)

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Since chiller plants consume a large portion of the energy use in the buildings with HVAC systems, growing attention has been paid to chiller plant optimization. A typical chiller plant includes devices such as chillers, cooling towers, primary pumps and condenser pumps. Operation settings of a device are zeros when the device is off; otherwise, they are within positive ranges. With nonlinearity in heat exchange, chiller plant optimization is a mixed-integer nonlinear problem. Establishing a problem formulation with a good balance between accuracy and simplicity is usually difficult. For example, water temperature is critical in improving chiller efficiency while chiller power consumption is a highly nonlinear function of the temperature. In this paper, for simplicity, devices of the same class are assumed identical. To save energy and simplify the problem, a formulation with chilled water supply temperature as an additional decision variable and condenser water supply temperature as a parameter is established. To obtain good solutions and save computational effort, surrogate Lagrangian relaxation (SLR) combined with sequential quadratic programming (SQP) with good initialization is used. Numerical testing shows that power consumption is significantly reduced with maximum savings around 18% in a partial load condition by using our method as compared with a baseline using current strategies.Index Terms -chiller plant optimization, surrogate Lagrangian relaxation, sequential quadratic programming.

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Section: Solution Methodologymentioning

confidence: 99%

Section: Constraints Of Primary Pumpsmentioning

confidence: 99%

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A decomposition and coordination-based method for chiller plant optimization

Zhang

Luh

Fan³

et al. 2015

2015 International Conference on Complex Systems Engineering (ICCSE)

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“…To reduce the conservativeness of the interval CCUC model, this section focuses on improving the computing of RHS intervals in (15), (16), (20), and (21). Section IV will further alleviate the overall conservatives through shrinking the input intervals of GSFs.…”

Section: Improved Interval Computationmentioning

confidence: 99%

“…Such an identification method for deterministic transmissionconstrained UC [15] is extended to consider uncertain renewables via interval modeling. To efficiently solve largescale MILP problems, Section V develops a solution methodology using Surrogate Lagrangian Relaxation (SLR) [16] and branch-and-cut (B&C) [17].…”

mentioning

confidence: 99%

Transmission Contingency-Constrained Unit Commitment with High Penetration of Renewables via Interval Optimization

Luh

Litvinov³

et al. 2016

IEEE Trans. Power Syst.

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A generalized proportional‐integral observer for fault detection: An approximate input disturbance decoupling approach

Dai

Cui

et al. 2023

Adaptive Control & Signal

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Summary This article proposes a generalized PI observer with approximate disturbance decoupling (ADD‐GPIO) for detecting incipient actuator faults of a system subject to periodic input disturbances. Robustness to disturbances and sensitivity to faults is achieved through dynamic configuration of the disturbance transmission zeros and pole‐optimization respectively. By incorporating the v$$ v $$‐gap metric with Hprefix−$$ {H}_{-} $$ index, a novel interpretable fault sensitivity optimization objective function is proposed. It is the first time in the fault detection observer design that the difference between the transfer function matrices (TFMs) relating fault detection residual to the disturbances and faults is quantified by the proposed v$$ v $$‐gap metric, which allows a more differentiated treatment of the disturbance and fault signals for better fault detection. Then, the optimal design of the ADD‐GPIO is modeled as a mixed‐integer optimization problem and the Lagrangian relaxation is adopted to find the near‐optimal parameters of the ADD‐GPIO at less computation costs in real application. Finally, both simulation and lab experiments of a two‐wheeled self‐balancing robot are carried out to validate the improved performance of the proposed method.

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Convergence of the Surrogate Lagrangian Relaxation Method

Cited by 138 publications

References 30 publications

A decomposition and coordination-based method for chiller plant optimization

A decomposition and coordination-based method for chiller plant optimization

Transmission Contingency-Constrained Unit Commitment with High Penetration of Renewables via Interval Optimization

A generalized proportional‐integral observer for fault detection: An approximate input disturbance decoupling approach

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