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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
A robust SQP method for mathematical programs with linear complementarity constraints
 Computational Optimization and Applications
, 2003
"... Abstract. The relationship between the mathematical program with linear complementarity constraints (MPCC) and its inequality relaxation is studied. A new sequential quadratic programming (SQP) method is presented for solving the MPCC based on this relationship. A certain SQP technique is introduced ..."
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Cited by 8 (0 self)
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Abstract. The relationship between the mathematical program with linear complementarity constraints (MPCC) and its inequality relaxation is studied. A new sequential quadratic programming (SQP) method is presented for solving the MPCC based on this relationship. A certain SQP technique
An NE/SQP Method for the Bounded Nonlinear Complementarity Problem
 Preprint MCSP5080495, Argonne National Laboratory, Argonne
, 1995
"... NE/SQP is a recent algorithm that has proven quite effective for solving the pure and mixed forms of the nonlinear complementarity problem (NCP). NE/SQP is robust in the sense that its directionfinding subproblems are always solvable; in addition, the convergence rate of this method is Qquadratic. ..."
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Cited by 2 (2 self)
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quadratic. In this paper we consider a generalized version of NE/SQP proposed by Pang and Qi, that is suitable for the bounded NCP. We extend their work by demonstrating a stronger convergence result and then test a proposed method on several numerical problems. Key Words: Nonlinear complementarity problem, mathematical
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
Equations with Semismooth Jacobians and Nonlinear Complementarity Problems
"... We dedicate this paper to Steve Robinson on the occasion of his 65th birthday, in recognition of his remarkable scholarly accomplishments and in appreciation for his collegiality, guidance, and kindness. Received: date / Accepted: date Abstract We discuss local convergence of Newton’s method to a si ..."
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equations reformulation of the nonlinear complementarity problem (NCP) whose derivative is strongly semismooth when the function f arising in the NCP is sufficiently smooth. Conditions on f are derived that ensure that the appropriate regularity conditions are satisfied for the nonlinearequations reformulation
Results 1  10
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43,911