Numerical experience with sequential quadratic programming algorithms for equality constrained nonlinear programming

ABSTRACT

Computational experience is given for a sequential quadratic programming algorithm when LaGrange multiplier estimates, Hessian approximations, and merit functions are varied to test for computational efficiency. Indications of areas for further research are given.

REFERENCES

• 1: BOGGS, P. T., AND TOLLE, J.W. A family of descent functions for constrained optimization. SIAM J. Numer. Anal. 21 (Dec. 1984), 1146-1161.
• 2: Paul T. Boggs , Jon W. Tolle, A strategy for global convergence in a sequential quadratic programming algorithm, SIAM Journal on Numerical Analysis, v.26 n.3, p.600-623, June 1989 [doi>10.1137/0726036]
• 3: CELIS, M. R., DENNIS, J. E., AND TAPIA, R.A. A trust region strategy for nonlinear equality constrained optimization. In Numerical Optimization, 1984. P. T. Boggs, R. H. Byrd, and R. B. Schnabel, Eds. SIAM, Philadelphia, 1985, 71-82.
• 4: CHAMBERLAIN, R. M., LEMARECHAL, C., PEDERSEN, H. C., AND POWELL, M. J. D. The watchdog technique for forcing convergence in algorithms for constrained optimization. Math. Program. Stud. 16 (Mar. 1982), 1-17.
• 5: COLEMAN, T., AND CONN, A. On the local convergence of a quasi-Newton method for the nonlinear programming problem. SIAM J. Namer. Anal. 21 (Aug. 1984), 755-769.
• 6: DI PILLO, G., AND GRIPPO, L. A new class of augmented Lagrangians in nonlinear programming. SIAM J. Control Opt. 17 (Sept. 1979), 618-628.
• 7: FONTECILLA, R. A general convergence theory for quasi-Newton methods for constrained optimization. Ph.D. dissertation, Mathematical Sciences Dept., Rice Univ., Houston, Tex., 1983.
• 8: GLAD, S. T. Properties of updating methods for the multiplies in augmented Lagrangians. J. Optim. Theor. Appl. 28 (June 1979), 135-156.
• 9: HAN, S.P. Superlinearly convergent variable metric algorithms for general nonlinear programming problems. Math. Program. 11 (Dec. 1976), 263-282.
• 10: NOCEDAL, Z., AND OVERTON, M. Projected Hessian updating algorithms for nonlinearly constrained optimization. To appear in SIAM J. Numer. Anal.
• 11: POWELL, M. J.D. Algorithms for nonlinear constraints that use Lagrangian functions. Math. Program. 14 (Mar. 1978), 224-248.
• 12: POWELL, M. J.D. The performance of two subroutines for constrained optimization on some difficult test problems. In Numerical Optimization I984. P. T. Boggs, R. H. Byrd, and R. B. Schnabel, Eds. SIAM, Philadelphia, 1985, 160-177.
• 13: M J D Powell , Y Yuan, A recursive quadratic programming algorithm that uses differentiable exact penalty functions, Mathematical Programming: Series A and B, v.35 n.3, p.265-278, July 1986 [doi>10.1007/BF01580880]
• 14: SCHITTKOWSKI, K. The nonlinear programming method of Wilson, Han, and Powell with an augmented Lagrangian type line search function, Part I: Convergence analysis. Numer. Math 38, 1 (1981), 83-114.
• 15: TAPIA, R. A. Diagonalized multiplier methods and quasi-Newton methods for constrained optimization. J. Optim. Theor. Appl. 22 (June 1977), 135-184.
• 16: TAPIA, R.A. Quasi-Newton method for equality constraint optimization: Equivalence of existing methods and a new implementation. Nonlinear Programming 3. O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, Eds. Academic Press, New York, 1978, 125-164.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.6 Optimization
          Subjects: Nonlinear programming

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.6 Optimization
          Subjects: Constrained optimization

General Terms:
Algorithms