A trust-region method by active-set strategy for general nonlinear optimization

The paper explores a trust-region active-set algorithm for general nonlinear optimization with nonlinear equality and inequality constraints. In this algorithm, an active-set strategy is used together with trust-region methods to compute the trial step. L"1 penalty functions are employed to obtain the global convergence. The global convergence of this algorithm is proved under standard conditions. The numerical tests show the efficiency of the proposed algorithm.

[1]  Jorge J. Moré,et al.  Computing a Trust Region Step , 1983 .

[2]  Z. W. Chen,et al.  Nonmonotone Trust-Region Method for Nonlinear Programming with General Constraints and Simple Bounds , 2004 .

[3]  A. Vardi A Trust Region Algorithm for Equality Constrained Minimization: Convergence Properties and Implementation , 1985 .

[4]  A. Vardi,et al.  New minimax algorithm , 1984 .

[5]  Le Thi Hoai An,et al.  A Combined D.C. Optimization—Ellipsoidal Branch-and-Bound Algorithm for Solving Nonconvex Quadratic Programming Problems , 1998, J. Comb. Optim..

[6]  Andrew R. Conn,et al.  Second-order conditions for an exact penalty function , 1980, Math. Program..

[7]  Ke Su,et al.  A modified SQP method and its global convergence , 2007, Appl. Math. Comput..

[8]  Ya-Xiang Yuan,et al.  A trust region algorithm for equality constrained optimization , 1990, Math. Program..

[9]  José Mario Martínez,et al.  Nonlinear programming algorithms using trust regions and augmented Lagrangians with nonmonotone penalty parameters , 1999, Math. Program..

[10]  M. R. Celis A TRUST REGION STRATEGY FOR NONLINEAR EQUALITY CONSTRAINED OPTIMIZATION (NONLINEAR PROGRAMMING, SEQUENTIAL QUADRATIC) , 1985 .

[11]  Shih-Ping Han A globally convergent method for nonlinear programming , 1975 .

[12]  Richard H. Byrd,et al.  A Trust Region Algorithm for Nonlinearly Constrained Optimization , 1987 .

[13]  R. Fletcher Practical Methods of Optimization , 1988 .

[14]  Le Thi Hoai An,et al.  A Branch and Bound Method via d.c. Optimization Algorithms and Ellipsoidal Technique for Box Constrained Nonconvex Quadratic Problems , 1998, J. Glob. Optim..

[15]  Ya-Xiang Yuan,et al.  Optimization theory and methods , 2006 .