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TrustRegion InteriorPoint SQP Algorithms For A Class Of Nonlinear Programming Problems
 SIAM J. CONTROL OPTIM
, 1997
"... In this paper a family of trustregion interiorpoint SQP algorithms for the solution of a class of minimization problems with nonlinear equality constraints and simple bounds on some of the variables is described and analyzed. Such nonlinear programs arise e.g. from the discretization of optimal co ..."
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Cited by 35 (8 self)
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In this paper a family of trustregion interiorpoint SQP algorithms for the solution of a class of minimization problems with nonlinear equality constraints and simple bounds on some of the variables is described and analyzed. Such nonlinear programs arise e.g. from the discretization of optimal control problems. The algorithms treat states and controls as independent variables. They are designed to take advantage of the structure of the problem. In particular they do not rely on matrix factorizations of the linearized constraints, but use solutions of the linearized state equation and the adjoint equation. They are well suited for large scale problems arising from optimal control problems governed by partial differential equations. The algorithms keep strict feasibility with respect to the bound constraints by using an affine scaling method proposed for a different class of problems by Coleman and Li and they exploit trustregion techniques for equalityconstrained optimizatio...
Semismooth Newton methods for operator equations in function spaces
, 2000
"... We develop a semismoothness concept for nonsmooth superposition operators in function spaces. The considered class of operators includes NCPfunctionbased reformulations of infinitedimensional nonlinear complementarity problems, and thus covers a very comprehensive class of applications. Our resul ..."
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Cited by 28 (3 self)
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We develop a semismoothness concept for nonsmooth superposition operators in function spaces. The considered class of operators includes NCPfunctionbased reformulations of infinitedimensional nonlinear complementarity problems, and thus covers a very comprehensive class of applications. Our results generalize semismoothness and fforder semismoothness from finitedimensional spaces to a Banach space setting. Hereby, a new generalized differential is used that can be seen as an extension of Qi's finitedimensional Csubdifferential to our infinitedimensional framework. We apply these semismoothness results to develop a Newtonlike method for nonsmooth operator equations and prove its local qsuperlinear convergence to regular solutions. If the underlying operator is fforder semismoothness, convergence of qorder 1 + ff is proved. We also establish the semismoothness of composite operators and develop corresponding chain rules. The developed theory is accompanied by illustrating e...
NonMonotone TrustRegion Methods for BoundConstrained Semismooth Equations with Applications to Nonlinear Mixed Complementarity Problems
, 1999
"... We develop and analyze a class of trustregion methods for boundconstrained semismooth systems of equations. The algorithm is based on a simply constrained differentiable minimization reformulation. Our global convergence results are developed in a very general setting that allows for nonmonotoni ..."
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Cited by 14 (4 self)
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We develop and analyze a class of trustregion methods for boundconstrained semismooth systems of equations. The algorithm is based on a simply constrained differentiable minimization reformulation. Our global convergence results are developed in a very general setting that allows for nonmonotonicity of the function values at subsequent iterates. We propose a way of computing trial steps by a semismooth Newtonlike method that is augmented by a projection onto the feasible set. Under a DennisMoretype condition we prove that close to a BDregular solution the trustregion algorithm turns into this projected Newton method, which is shown to converge locally qsuperlinearly or quadratically, respectively, depending on the quality of the approximate BDsubdifferentials used. As an important application we discuss in detail how the developed algorithm can be used to solve nonlinear mixed complementarity problems (MCPs). Hereby, the MCP is converted into a boundconstrained semismooth...
Superlinear and Quadratic Convergence of AffineScaling InteriorPoint Newton Methods for Problems with Simple Bounds without Strict Complementarity Assumption
, 1998
"... A class of affinescaling interiorpoint methods for bound constrained optimization problems is introduced which are locally qsuperlinear or qquadratic convergent. It is assumed that the strong... ..."
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Cited by 12 (3 self)
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A class of affinescaling interiorpoint methods for bound constrained optimization problems is introduced which are locally qsuperlinear or qquadratic convergent. It is assumed that the strong...
On the Interplay Between Interior Point Approximation and Parametric Sensitivities in Optimal Control ∗
, 2005
"... This paper is concerned with the sensitivities of function space oriented interior point approximations in parameter dependent optimization problems. For an abstract setting that covers control constrained optimal control problems, the convergence of interior point sensitivities to the sensitivities ..."
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Cited by 1 (0 self)
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This paper is concerned with the sensitivities of function space oriented interior point approximations in parameter dependent optimization problems. For an abstract setting that covers control constrained optimal control problems, the convergence of interior point sensitivities to the sensitivities of the optimal solution is shown. Error bounds for Lq norms are derived and illustrated with numerical examples.
ÉquipesProjets Commands
"... apport de recherche ISSN 02496399 ISRN INRIA/RR7126FR+ENGinria00436768, version 1 27 Nov 2009Asymptotic expansion for the solution of a penalized control constrained semilinear elliptic problems ..."
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apport de recherche ISSN 02496399 ISRN INRIA/RR7126FR+ENGinria00436768, version 1 27 Nov 2009Asymptotic expansion for the solution of a penalized control constrained semilinear elliptic problems
MINIMUM WEIGHT TOPOLOGY OPTIMIZATION SUBJECT TO UNSTEADY HEAT EQUATION AND SPACETIME POINTWISE CONSTRAINTS – TOWARD AUTOMATIC OPTIMAL RISER DESIGN IN THE SHAPE CASTING PROCESS
"... Abstract. The automatic optimal design of feeding system in the shape casting process is considered, i.e., to find the optimal position, size, shape and topology of risers, and risernecks. It is formulated as a minimum weight topology optimization problem subjected to a nonlinear transient PDE and ..."
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Abstract. The automatic optimal design of feeding system in the shape casting process is considered, i.e., to find the optimal position, size, shape and topology of risers, and risernecks. It is formulated as a minimum weight topology optimization problem subjected to a nonlinear transient PDE and an infinite number of spacetime pointwise constraints. In addition to regularization and relaxation of the original model, an elegant bilevel reformulation of the optimization problem is introduced which makes it possible to manage the infinite number of design parameters and stateconstraints efficiently. The computational cost of this method is asymptotically independent from the number of design parameters and constraints. The validity and efficiency of the presented method are supported by several examples, from simple benchmarks to complex industrial castings. According to our numerical results, the presented approach makes a relatively complete solution to the problem of automatic optimal rider design in the shape casting process.