A sequential quadratic programming (SQP) algorithm generating feasible iterates is described and analyzed. What distinguishes this algorithm from previous feasible SQP algorithms proposed by various authors is a reduction in the amount of computation required to generate a new iterate while the proposed scheme still enjoys the same global and fast local convergence properties. A preliminary implementation has been tested and some promising numerical results are reported.

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A Computationally Efficient Feasible Sequential Quadratic Programming Algorithm

Semi-Infinite Programming

This paper provides a review of numerical methods for the solution of smooth semi-infinite programming problems. Fundamental and partly new results on level sets, discretization, and local reduction are presented in a primary section. References to algorithms for real and complex continuous Chebyshev approximation are given for historical reasons and in order to point out connections.

Numerical Methods for Semi-Infinite Programming: A Survey

In this article, we examine the solution of minimum-effort optimal control problems for open-chain manipulators. An approximate Solution to the optimal control problem is determined by a constrained parameter optimization over a set of B-spline basis functions. We demonstrate that the parameter-optimization formulation of the problem is numerically ill-conditioned, and that it is therefore essential to include analytic, or exact, gradients of the objective fiunction and the constraints in order to guarantee a solution. A recursive expression for these gradients is developed for general serial chains. Constraints on end-effector motions are taken into account using the logarithmn of the spatial displacement. Our formulation relies on the use of matrix exponentials for the manipulator kinematics, dynamics, and task constraints. Several examples are presented that demostrate the power and flexibility of our approach.

Minimum-Effort Motions for Open-Chain Manipulators with Task-Dependent End-Effector Constraints

In the first part of this paper, we prove the convergence of a class of discretization methods for the solution of nonlinear semi-infinite programming problems, which includes known methods for linear problems as special cases. In the second part, we modify and study this type of algorithms for linear problems and suggest a specific method which requires the solution of a quadratic programming problem at each iteration. With this algorithm, satisfactory results can also be obtained for a number of singular problems. We demonstrate the performance of the algorithm by several numerical examples of multivariate Chebyshev approximation problems.

Discretization methods for the solution of semi-infinite programming problems

For linear semi-infinite programming problems a discretization method is presented. A first coarse grid is successively refined in such a way that the solution on the foregoing grids can be used on the one hand as starting points for the subsequent grids and on the other hand to considerably reduce the number of constraints which have to be considered in the subsequent problems. This enables an efficient treatment of large problems with moderate storage requirements. A numerically stable Simplex-algorithm is used to solve the LP-subproblems. Numerical examples from bivariate Chebyshev approximation are presented.

An implementation of a discretization method for semi-infinite programming

For convex quadratic semi-infinite programming problems aFortran-package is described. A first coarse grid is successively refined in such a way that the solution on the foregoing grids can be used on the one hand as starting points for the subsequent grids and on the other hand to considerably reduce the number of constraints which have to be considered in the subsequent problems. This enables an efficient treatment of large problems with moderate storage requirements. Powell's (1983) numerically stable convex quadratic programming implementation is used to solve the QP-subproblems.

R. Hettich

Papers

An implementation of a discretization method for semi-infinite programming

A note on an implementation of a method for quadratic semi-infinite programming