Approximating the objective function׳s gradient using perceptrons for constrained minimization with application in drag reduction

• Published in: Computers & operations research Vol. 64; pp. 139 - 158
• Main Authors: Kocuk, Burak, Altınel, İ. Kuban, Aras, Necati
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.12.2015; Pergamon Press Inc
• Subjects: Algorithms; Approximation; Constrained optimization; Drag reduction; Mathematical problems; Neural networks; Operations research; Reduced gradient; Shear stress; Studies; Turbulence; Reduced gradient; Shear stress; Turbulence; Drag reduction; Neural networks; Constrained optimization
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2015.05.012

This paper is concerned with the minimization of a function whose closed-form analytical expression is unknown, subject to well-defined and differentiable constraints. We assume that there is available data to train a multi-layer perceptron, which can be used for estimating the gradient of the objective function. We combine this estimate with the gradients of the constraints to approximate the reduced gradient, which is ultimately used for determining a feasible descent direction. We call this variant of the reduced gradient method as the Neural Reduced Gradient algorithm. We evaluate its performance on a large set of constrained convex and nonconvex test problems. We also provide an interesting and important application of the new method in the minimization of shear stress for drag reduction in the control of turbulence. •Considers nonlinear constrained minimization with unknown objective function.•Introduces a perceptron based method to estimate the gradient of the objective.•Proposes a neural reduced gradient algorithm to compute a stationary point.•Applies the new method to shear stress minimization for reducing the turbulence.