Solving linear and quadratic programs with an analog circuit

Vichik, Sergey; Borrelli, Francesco

doi:10.1016/j.compchemeng.2014.01.011

Cited by 32 publications

(20 citation statements)

References 27 publications

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“…By composing the elementary circuits of the previous section we can design an analog circuit which implements the constraints A eq V = b eq and A ineq V ≤ b ineq . By using simple energy arguments, in [17] it was shown that such circuit would minimize a cost function…”

Section: Quadratic Cost Functionmentioning

confidence: 99%

“…, a constant voltage source and a diode for inequality nodes. [17] for additional details). The redundant constraints are implemented using a simple circuit depicted in Fig.…”

Section: Quadratic Cost Functionmentioning

confidence: 99%

“…In [17] we presented the design of an analog QP circuit. We showed that its equilibrium voltages are the QP optimizers.…”

Section: Introductionmentioning

confidence: 99%

“…For the sake of better readability, a description of how to construct an analog circuit from a given QP is presented in Section 2. For more details and experimental results we refer the reader to the description in [17]. Section 3 presents stability analysis of the circuit and the main result of the paper.…”

Section: Introductionmentioning

confidence: 99%

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Stability of an analog optimization circuit for quadratic programming

Vichik

Arcak

Borrelli

2016

Systems & Control Letters

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We study the stability of an analog optimization circuit that solves quadratic programming (QP) problems. The circuit dynamics are modeled as a switched affine system. A piece-wise quadratic Lyapunov function and the KYP lemma are used to derive the stability criterion. The stability criterion characterizes the range of critical circuit parameters for which the QP circuit is globally exponentially stable.

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Section: Quadratic Cost Functionmentioning

confidence: 99%

“…, a constant voltage source and a diode for inequality nodes. [17] for additional details). The redundant constraints are implemented using a simple circuit depicted in Fig.…”

Section: Quadratic Cost Functionmentioning

confidence: 99%

“…In [17] we presented the design of an analog QP circuit. We showed that its equilibrium voltages are the QP optimizers.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stability of an analog optimization circuit for quadratic programming

Vichik

Arcak

Borrelli

2016

Systems & Control Letters

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“…More relevant to our work, Vichik and Borrelli design an analog circuit to solve linear and quadratic programming problem, where unknown variables are directly modeled by node voltages and each constraint is specified by a dedicated circuit component [30]. The node voltages representing unknown variables are driven towards their optimal value subjected to the circuit constraints.…”

Section: Related Workmentioning

confidence: 99%

A reconfigurable analog substrate for highly efficient maximum flow computation

Liu

Zhang

2015

Proceedings of the 52nd Annual Design Automation Conference

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We present the design and analysis of a novel analog reconfigurable substrate that enables fast and efficient computation of maximum flow on directed graphs. The substrate is composed of memristors and standard analog circuit components, where the on/off states of the crossbar switches encode the graph topology. We show that upon convergence, the steady-state voltages in the circuit capture the solution to the maximum flow problem. We also provide techniques to minimize the impacts of variability and non-ideal circuit components on the solution quality, enabling practical implementation of the proposed substrate. Performance evaluation demonstrates orders of magnitude improvements in speed and energy efficiency compared to a standard CPU implementation.

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Ultrafast Hybrid Computing Systems Enabled by Memristor‐Based Quadratic Programming Circuits

Liu,

Cheng,

Hossain

et al. 2024

Adv Funct Materials

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Implementing algorithms purely on digital computing platforms dramatically halts the performance of conventional computing systems. Revolutionary computing systems with extreme energy efficiency and high accuracy are demanded to handle the growing computing tasks. Here, the research on hybrid analog–digital computing platforms enabled by memristor‐based optimization solvers for achieving ultrafast computations is presented. By utilizing tunable memristors as parameters to solve linear programming (LP) and quadratic programming (QP) problems, a real‐time control algorithm for micro air vehicles (MAVs) and a support vector machine (SVM) algorithm for cancer diagnosis are implemented. These experiments demonstrate over 2000x speed‐up compared to conventional digital platforms, with negligible energy consumption, using a memristor‐based system consisting of six memristors. These findings underscore the vast potential of memristor‐based optimization solvers not only in hybrid analog–digital computing platforms but also as a transformative solution for a wide range of modern computing challenges. This approach promises significant advancements in energy efficiency and ultrafast speed, positioning it as a leading contender for next‐generation computing paradigms.

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Solving linear and quadratic programs with an analog circuit

Cited by 32 publications

References 27 publications

Stability of an analog optimization circuit for quadratic programming

Stability of an analog optimization circuit for quadratic programming

A reconfigurable analog substrate for highly efficient maximum flow computation

Ultrafast Hybrid Computing Systems Enabled by Memristor‐Based Quadratic Programming Circuits

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