Second-Order-Cone Constraints for Extended Trust-Region Subproblems
نویسندگان
چکیده
منابع مشابه
Second-Order-Cone Constraints for Extended Trust-Region Subproblems
The classical trust-region subproblem (TRS) minimizes a nonconvex quadratic objective over the unit ball. In this paper, we consider extensions of TRS having extra constraints. When two parallel cuts are added to TRS, we show that the resulting nonconvex problem has an exact representation as a semidefinite program with additional linear and second-order-cone constraints. For the case where an ...
متن کاملThe solution of Euclidean norm trust region SQP subproblems via second order cone programs, an overview and elementary introduction
It is well known that convex SQP subproblems with a Euclidean norm trust region constraint can be reduced to second order cone programs for which the theory of Euclidean Jordan-algebras leads to efficient interior-point algorithms. Here, a brief and self-contained outline of the principles of such an implementation is given. All identities relevant for the implementation are derived from scratc...
متن کاملOn solving L-SR1 trust-region subproblems
In this article, we consider solvers for large-scale trust-region subproblems when the quadratic model is defined by a limited-memory symmetric rank-one (L-SR1) quasi-Newton matrix. We propose a solver that exploits the compact representation of L-SR1 matrices. Our approach makes use of both an orthonormal basis for the eigenspace of the L-SR1 matrix and the ShermanMorrison-Woodbury formula to ...
متن کاملSl1QP Based Algorithm with Trust Region Technique for Solving Nonlinear Second-Order Cone Programming Problems
In this paper, we propose an algorithm based on Fletcher’s Sl1QP method and the trust region technique for solving Nonlinear Second-Order Cone Programming (NSOCP) problems. The Sl1QP method was originally developed for nonlinear optimization problems with inequality constraints. It converts a constrained optimization problem into an unconstrained problem by using the l1 exact penalty function, ...
متن کاملA Second-Order Cone Based Approach for Solving the Trust-Region Subproblem and Its Variants
We study the trust region subproblem (TRS) of minimizing a nonconvex quadratic function over the unit ball with additional conic constraints. Despite having a nonconvex objective, it is known that the TRS and a number of its variants are polynomial-time solvable. In this paper, we follow a second-order cone based approach to derive an exact convex formulation of the TRS, and under slightly stro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2013
ISSN: 1052-6234,1095-7189
DOI: 10.1137/110826862