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SEMISMOOTH SQP METHOD FOR EQUALITYCONSTRAINED OPTIMIZATION PROBLEMS WITH AN APPLICATION TO THE LIFTED REFORMULATION OF MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS
, 2010
"... We consider the sequential quadratic programming algorithm (SQP) applied to equalityconstrained optimization problems, where the problem data is differentiable with Lipschitzcontinuous first derivatives. For this setting, DennisMoré type analysis of primal superlinear convergence is presented. Our ..."
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Cited by 2 (2 self)
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main motivation is a special modification of SQP tailored to the structure of the lifted reformulation of mathematical programs with complementarity constraints (MPCC). For this problem, we propose a special positive definite modification of the matrices in the generalized Hessian, which is suitable
RESEARCH ARTICLE Semismooth SQP Method for EqualityConstrained Optimization Problems with an Application to the Lifted Reformulation of Mathematical Programs with Complementarity Constraints
, 2010
"... We consider the sequential quadratic programming algorithm (SQP) applied to equalityconstrained optimization problems, where the problem data is differentiable with Lipschitzcontinuous first derivatives. For this setting, DennisMoré type analysis of primal superlinear convergence is presented. Our ..."
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main motivation is a special modification of SQP tailored to the structure of the lifted reformulation of mathematical programs with complementarity constraints (MPCC). For this problem, we propose a special positive definite modification of the matrices in the generalized Hessian, which is suitable
Semismooth Newton method for the lifted reformulation of mathematical programs with complementarity constraints
, 2009
"... We consider a reformulation of mathematical programs with complementarity constraints, where by introducing an artificial variable the constraints are converted into equalities which are once but not twice differentiable. We show that the Lagrange optimality system of such a reformulation is semismo ..."
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Cited by 7 (5 self)
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We consider a reformulation of mathematical programs with complementarity constraints, where by introducing an artificial variable the constraints are converted into equalities which are once but not twice differentiable. We show that the Lagrange optimality system of such a reformulation
Sequential equalityconstrained optimization for nonlinear programming
, 2015
"... A new method is proposed for solving optimization problems with equality constraints and bounds on the variables. In the spirit of Sequential Quadratic Programming and Sequential LinearlyConstrained Programming, the new method approximately solves, at each iteration, an equalityconstrained optimiz ..."
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A new method is proposed for solving optimization problems with equality constraints and bounds on the variables. In the spirit of Sequential Quadratic Programming and Sequential LinearlyConstrained Programming, the new method approximately solves, at each iteration, an equalityconstrained
SEMISMOOTH METHODS FOR LINEAR AND NONLINEAR
, 2006
"... The optimality conditions of a nonlinear secondorder cone program can be reformulated as a nonsmooth system of equations using a projection mapping. This allows the application of nonsmooth Newton methods for the solution of the nonlinear secondorder cone program. Conditions for the local quadra ..."
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The optimality conditions of a nonlinear secondorder cone program can be reformulated as a nonsmooth system of equations using a projection mapping. This allows the application of nonsmooth Newton methods for the solution of the nonlinear secondorder cone program. Conditions for the local
HESSIANFREE METHODS FOR CHECKING THE SECONDORDER SUFFICIENT CONDITIONS IN EQUALITYCONSTRAINED OPTIMIZATION AND EQUILIBRIUM PROBLEMS
"... Abstract. Verifying the SecondOrder Sufficient Condition (SOSC), thus ensuring a stationary point locally minimizes a given objective function (subject to certain constraints), is an essential component of nonconvex computational optimization and equilibrium programming. This article proposes th ..."
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Abstract. Verifying the SecondOrder Sufficient Condition (SOSC), thus ensuring a stationary point locally minimizes a given objective function (subject to certain constraints), is an essential component of nonconvex computational optimization and equilibrium programming. This article proposes
Applications of Reformulations in Mathematical Programming
, 2012
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Solving mathematical programs with complementarity constraints with nonlinear solvers
 Recent Advances in Optimization. Lecture Notes in Economics and Mathematical Systems
"... tmQdps. uminho. pt Summary. MPCC can be solved with specific MPCC codes or in its nonlinear equivalent formulation (NLP) using NLP solvers. Two NLP solvers NPSOL and the line search filter SQP are used to solve a collection of test problems in AMPL. Both are based on SQP (Sequential Quadratic Prog ..."
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Cited by 1 (0 self)
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tmQdps. uminho. pt Summary. MPCC can be solved with specific MPCC codes or in its nonlinear equivalent formulation (NLP) using NLP solvers. Two NLP solvers NPSOL and the line search filter SQP are used to solve a collection of test problems in AMPL. Both are based on SQP (Sequential Quadratic
Semismooth Equations ∗
"... [Article] Hybrid Newtontype method for a class of semismooth equations ..."
An `1 Elastic InteriorPoint Methods for Mathematical Programs with Complementarity Constraints
, 2009
"... Abstract. We propose an interiorpoint algorithm based on an elastic formulation of the `1penalty merit function for mathematical programs with complementarity constraints. The method generalizes that of Gould, Orban, and Toint (2003) and naturally converges to a strongly stationary point or delive ..."
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Abstract. We propose an interiorpoint algorithm based on an elastic formulation of the `1penalty merit function for mathematical programs with complementarity constraints. The method generalizes that of Gould, Orban, and Toint (2003) and naturally converges to a strongly stationary point
Results 1  10
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