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Sequential Quadratic Programming
, 1995
"... this paper we examine the underlying ideas of the SQP method and the theory that establishes it as a framework from which effective algorithms can ..."
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Cited by 114 (2 self)
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this paper we examine the underlying ideas of the SQP method and the theory that establishes it as a framework from which effective algorithms can
A New Trust Region Algorithm For Equality Constrained Optimization
, 1995
"... . We present a new trust region algorithm for solving nonlinear equality constrained optimization problems. At each iterate a change of variables is performed to improve the ability of the algorithm to follow the constraint level sets. The algorithm employs L 2 penalty functions for obtaining global ..."
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Cited by 51 (7 self)
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. We present a new trust region algorithm for solving nonlinear equality constrained optimization problems. At each iterate a change of variables is performed to improve the ability of the algorithm to follow the constraint level sets. The algorithm employs L 2 penalty functions for obtaining global convergence. Under certain assumptions we prove that this algorithm globally converges to a point satisfying the second order necessary optimality conditions; the local convergence rate is quadratic. Results of preliminary numerical experiments are presented. 1. Introduction. We consider the equality constrained optimization problem minimize f(x) subject to c(x) = 0 (1:1) where x 2 ! n and f : ! n ! !, and c : ! n ! ! m are smooth nonlinear functions. Problem (1.1) is often solved by successive quadratic programming (SQP) methods. At a current point x k 2 ! n , SQP methods determine a search direction d k by solving a quadratic programming problem minimize rf(x k ) T d + 1 2 ...
ArcLength Method for Frictional Contact Problems by using Mathematical Program with Complementarity Constraints
 Building Geoenvironment Engineering Laboratory, Kyoto University
, 2004
"... A new formulation as well as a new solution technique is proposed for equilibrium pathfollowing method in twodimensional quasistatic frictional contact problems. We consider the classical Coulomb friction law as well as geometrical nonlinearity explicitly. Based on a criterion of maximum dissipat ..."
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Cited by 2 (2 self)
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A new formulation as well as a new solution technique is proposed for equilibrium pathfollowing method in twodimensional quasistatic frictional contact problems. We consider the classical Coulomb friction law as well as geometrical nonlinearity explicitly. Based on a criterion of maximum dissipation of energy, we propose a mathematical program with complementarity constraints (MPEC) formulation in order to avoid unloading solutions in which most contact candidate nodes become stuck. A regularization scheme for the MPEC is proposed, which can be solved by using the conventional nonlinear programming approach. The equilibrium paths of various structures are computed in cases such that there exist some limit points and/or infinite number of successive bifurcation points. Keywords: contact problem, Coulomb's friction; arclength method, mathematical program with complementarity constraints (MPEC), maximum dissipation + Department of Urban and Environmental Engineering, Kyoto University email: kanno@archi.kyotou.ac.jp # Instituto Superior Tecnico, Dep. Eng. Civil and ICIST, Av. Rovisco Pais, 1049001 Lisboa, Portugal email: jmartins@civil.ist.utl.pt 1.
A QuasiNewton Quadratic Penalty Method For Minimization Subject To Nonlinear Equality Constraints
"... . We present a modified quadratic penalty function method for equality constrained optimization problems. The pivotal feature of our algorithm is that at every iterate we invoke a special change of variables to improve the ability of the algorithm to follow the constraint level sets. This change of ..."
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Cited by 1 (0 self)
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. We present a modified quadratic penalty function method for equality constrained optimization problems. The pivotal feature of our algorithm is that at every iterate we invoke a special change of variables to improve the ability of the algorithm to follow the constraint level sets. This change of variables gives rise to a suitable block diagonal approximation to the Hessian which is then used to construct a quasiNewton method. We show that the complete algorithm is globally convergent. Preliminary computational results are reported. Key words. nonlinearly constrained optimization, equality constraints, quasiNewton methods, BFGS, quadratic penalty function, reduced Hessian approximation AMS(MOS) subject classifications. 65K05, 65K10, 65H10, 90C30, 90C05, 68L10 1. Introduction. One of the great success stories in continuous optimization is the development of effective quasiNewton methods for unconstrained minimization (at least for problems of moderate size). Three important reas...
A QuasiNewton L2Penalty Method for Minimization Subject to Nonlinear Equality Constraints
"... . We present a modified L 2 penalty function method for equality constrained optimization problems. The pivotal feature of our algorithm is that at every iterate we invoke a special change of variables to improve the ability of the algorithm to follow the constraint level sets. This change of variab ..."
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. We present a modified L 2 penalty function method for equality constrained optimization problems. The pivotal feature of our algorithm is that at every iterate we invoke a special change of variables to improve the ability of the algorithm to follow the constraint level sets. This change of variables gives rise to a suitable block diagonal approximation to the Hessian which is then used to construct a quasiNewton method. We show that the complete algorithm is globally convergent with a local Qsuperlinearly convergence rate. Preliminary computational results are given for a few problems. 1. Introduction. We construct a quasiNewton L 2 penalty method for solving the equality constrained optimization problem minimize f(x) subject to c(x) = 0 (1:1) where x 2 ! n , and f : ! n ! ! and c : ! n ! ! m are smooth nonlinear functions. This method possesses both strong global convergence properties and a local superlinear convergence rate by combining an L 2 penalty function method ...
A Stablized SQP Method via Linear Equations
, 2000
"... . In this paper, we propose a stablized sequential quadratic programming (SSQP) method for solving general nonlinear constrained optimization problems (NLP). Most present locally quadratically convergent algorithms for solving NLP need to assume at least the linear independence constraint qualicatio ..."
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. In this paper, we propose a stablized sequential quadratic programming (SSQP) method for solving general nonlinear constrained optimization problems (NLP). Most present locally quadratically convergent algorithms for solving NLP need to assume at least the linear independence constraint qualication and sometimes also the strict complementarity condition. Some recently developed SSQP methods can achieve local quadratic convergence without assuming these two conditions. But at each step of these SSQP methods, one or several quadratic programming problems need to be solved. For the NewtonSSQP method proposed in this paper, not only it achieves local quadratic convergence without assuming the abovementioned two conditions, but also only one or several systems of linear equations need to be solved at each step. A characterization theorem for superlinear convergence of quasiNewtonSSQP methods is also given. Key Words. Constrained optimization problem, SSQP method, superlinear/quadrat...