94LVI Algorithms of OIpU (One-Iteration-per-Update) Type Handling Time-Dependent QP (Quadratic Programming) with Two Constraints

This paper presents three relatively effective numerical algorithms, i.e., 94LVI algorithms of OIpU (one-iteration-per-update) type, to handle time-dependent QP (quadratic programming) problems subject to two constraints respectively (i.e., equal-ity and inequality constraints, equality and bound constraints, or inequality and bound constraints). Specifically, two “bridges” play essential parts of the methods (i.e., the first “bridge” makes a QP problem convert to an LVI [linear variational inequality], and the second “bridge” makes the LVI convert to a PLPE [piecewise-linear projection equation]). On the basis of the standard 94LVI algorithm, the methods only update once through the solution of the previous sampling time node. Finally, we conduct a number of experiments to substantiate the three algorithms respectively, which use exponential functions, log functions, and trigonometric functions in corresponding coefficients of the experimental examples.