Finding all solutions of piecewise-linear resistive circuits using linear programming

Yamamura, Kenichiro; Ohshima, T.

doi:10.1109/81.669067

Cited by 62 publications

(46 citation statements)

References 18 publications

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“…Then, we extracted the characteristic curves from the small regions (boxes) and visualized them by the method described in footnote 11 of Reference [12].…”

Section: Finding All Characteristic Curvesmentioning

confidence: 99%

Finding all solutions of piecewise‐linear resistive circuits using the dual simplex method

Yamamura

Tanaka²

2002

Circuit Theory & Apps

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SUMMARYAn e cient algorithm is proposed for ÿnding all solutions of piecewise-linear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for non-existence of a solution to a system of PWL equations in a given region. In the conventional LP test, the system of PWL equations is transformed into an LP problem, to which the simplex method is applied. However, this algorithm requires a very large number of pivotings because the simplex method is applied on many regions. In this paper, we introduce the dual simplex method to the LP test, which makes the average number of pivotings per region much smaller (less than one, for example) and makes the algorithm very e cient. By numerical examples, it is shown that the proposed algorithm could ÿnd all solutions of large-scale problems, including those where the number of variables is 300 and the number of linear regions is 10 300 , in practical computation time.

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“…Then, we extracted the characteristic curves from the small regions (boxes) and visualized them by the method described in footnote 11 of Reference [12].…”

Section: Finding All Characteristic Curvesmentioning

confidence: 99%

Finding all solutions of piecewise‐linear resistive circuits using the dual simplex method

Yamamura

Tanaka²

2002

Circuit Theory & Apps

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“…The expression for is then easily found from the network, yielding (see also Fig. 3) or (8) We recall that (8) is only valid under the restriction and thus is an intermediate result, only valid within the context of (7), i.e., only valid to produce the solution for (5). Combining (7) with (8) …”

Section: A Network Examplementioning

confidence: 98%

“…The approaches proposed in the literature up until now solve this problem numerically for a given fixed value of the input sources. Regarding the numerical solution of PL resisitive circuits, methods as proposed in [7] and [8] can be used.…”

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confidence: 99%

Explicit formulas for the solutions of piecewise linear networks

Bokhoven

Leenaerts

1999

IEEE Trans. Circuits Syst. I

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Abstract-A methodology is presented for obtaining explicit formulas for the solution of class-P piecewise linear (PL) networks and, inherently, for the linear complementary problem (LCP). The method uses the b1c b1c b1c operator, which has been previously defined in the literature to extend the explicit PL model descriptions of Chua. An important consequence of the methodology is that it proves that class-P networks have explicit solutions.Index Terms-Constrained optimization, explicit solution algorithm, linear complementary problem, piecewise linear networks.

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“…The test using linear programming (LP) is one of the most powerful tests for nonexistence of a solution [16,20,21].…”

Section: Introductionmentioning

confidence: 99%

Finding all solutions of piecewise‐linear circuits by using linear programming

Yamamura

Tanaka²

2001

Electron Comm Jpn Pt III

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SUMMARYAn efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of PWL equations of the form Pg(x) + Qx s = 0 in a given region. In the LP test, the system of PWL equations is transformed into an LP problem, to which the simplex method is applied. Such an LP problem is obtained by surrounding the PWL functions by rectangles. In this paper, it is shown that the LP test can be performed very efficiently mostly by Phase II of the simplex method. Using the proposed techniques, the number of pivotings in the LP test becomes much smaller, which makes the algorithm very efficient. By numerical examples, it is shown that the proposed algorithm could find all solutions of relatively large scale circuits (

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Finding all solutions of piecewise-linear resistive circuits using linear programming

Cited by 62 publications

References 18 publications

Finding all solutions of piecewise‐linear resistive circuits using the dual simplex method

Finding all solutions of piecewise‐linear resistive circuits using the dual simplex method

Explicit formulas for the solutions of piecewise linear networks

Finding all solutions of piecewise‐linear circuits by using linear programming

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