Pshenichny’s Linearization Method for Mechanical System Optimization

Abstract

In 1970, Pshenichny published a linearization method for nonlinear programming in Russian, which has been overlooked in the English literature. The method is essentially a recursive quadratic programming technique with an active set strategy. Pshenichny has proved global convergence of the method and convergence rate estimates. The method is presented in this paper, with convergence theorems stated. Application of the method is made to shape optimal design, kinematic optimization, and dynamic system optimization. The method is shown to be particularly attractive in utilization of mechanical design sensitivity analysis techniques and performs well on all classes of problems treated.

Shape Optimal Design of an Engine Connecting Rod

“…Recent developments reported in reference [4] may be employed to improve accuracy of design sensitivity coefficients that are calculated with the aid of the finite element method, particulary for stress contraints near the boundary of the body. With more accurate design sensitivity results, much better optimization methods may be employed, e.g., a sequential quadratic programming method such as presented in reference [9].…”

Gradient-Based Trade-Off Design for Engineering Applications

“…The trade-off design is formulated in the framework of SQP. Traditionally, the SQP plays a key role in supporting direct search design optimization [8][9][10][11][12][13]. It aims to find the least change in the design variables that can reduce the objective function, f (x 0 ), and in the meantime, achieve the required corrections in the current values of the inequality constraints, g(x 0 ), and the equality ones, h(x 0 ).…”

“…The objection function in this approach is treated as part of the constraint set with the desired amount of reduction, ∆ f . Thus, the constraint set is expanded to include f as ∇g = ∇ f ∇g and g = ∆ f g (13) where g represents the initial constraint set. The amount, ∆ f , presented in Equation ( 13) is the same as that described in Equation (11).…”

Structural Sensitivity Analysis and Optimization 2

“…The linearization method LINRM [104] is used to solve the optimal design problem, and is based on a recursive quadratic programming algorithm. The linearization method LINRM [104] is used to solve the optimal design problem, and is based on a recursive quadratic programming algorithm.…”