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Gradient Projection Network: Analog Solver for Linearly Constrained Nonlinear Programming
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An analog approach is presented for solving nonlinear programming problems with linear constraint conditions. The present method is based on transformation of variables with exponential functions, which enables every trajectory to pass through an interior of feasible regions along a gradient direction projected onto the feasible space. Convergence of its trajectory to the solution of optimization problems is guaranteed and it is shown that the present scheme is an extension of the affine scaling method for linear programming to nonlinear programs under a slight modification of Riemannian metric. An analog electronic circuit is also presented that implements the proposed scheme in real time.
Title: Gradient Projection Network: Analog Solver for Linearly Constrained Nonlinear Programming
Description:
An analog approach is presented for solving nonlinear programming problems with linear constraint conditions.
The present method is based on transformation of variables with exponential functions, which enables every trajectory to pass through an interior of feasible regions along a gradient direction projected onto the feasible space.
Convergence of its trajectory to the solution of optimization problems is guaranteed and it is shown that the present scheme is an extension of the affine scaling method for linear programming to nonlinear programs under a slight modification of Riemannian metric.
An analog electronic circuit is also presented that implements the proposed scheme in real time.
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