Using sliding modes in static optimization and nonlinear programming

The paper is concerned with methods for solution of conventional optimization and mathematical programming problems [1–4] using discontinuous control algorithms. Deliberate introduction of sliding modes [5–7] into the system ensures that the output of the plant to be optimized follows the monotonically decreasing reference input, in the case of minimization, and that the constraints on the plant input parameters hold. This approach eliminates the need in hardware to obtain information on the gradients of the function to be optimized or constraining functions.The paper separately treats optimization algorithms without constraints on output parameters and with constraints of the equality and inequality types. The relation of the methods reported in the paper and gradient procedures for solution of mathematical programming problems using a special kind of penalty function is indicated.