New Results on Narrowing the Duality Gap of the Extended Celis-Dennis-Tapia Problem

In this paper, we consider the extended Celis--Dennis--Tapia (CDT) problem that has a positive duality gap. It is presented in theory that this positive duality gap can be narrowed by adding an app...

[1]  Michael L. Overton,et al.  Narrowing the difficulty gap for the Celis–Dennis–Tapia problem , 2015, Math. Program..

[2]  Ya-Xiang Yuan,et al.  On a subproblem of trust region algorithms for constrained optimization , 1990, Math. Program..

[3]  Samuel Burer,et al.  Second-Order-Cone Constraints for Extended Trust-Region Subproblems , 2013, SIAM J. Optim..

[4]  M. R. Celis.  A TRUST REGION STRATEGY FOR NONLINEAR EQUALITY CONSTRAINED OPTIMIZATION (NONLINEAR PROGRAMMING, SEQUENTIAL QUADRATIC) , 1985 .

[5]  Shuzhong Zhang,et al.  New Results on Quadratic Minimization , 2003, SIAM J. Optim..

[6]  Shuzhong Zhang,et al.  On Cones of Nonnegative Quadratic Functions , 2003, Math. Oper. Res..

[7]  Akiko Takeda,et al.  Solving Generalized CDT Problems via Two-Parameter Eigenvalues , 2016, SIAM J. Optim..

[8]  Yonina C. Eldar,et al.  Strong Duality in Nonconvex Quadratic Optimization with Two Quadratic Constraints , 2006, SIAM J. Optim..

[9]  Shuzhong Zhang,et al.  Strong Duality for the CDT Subproblem: A Necessary and Sufficient Condition , 2008, SIAM J. Optim..

[10]  Samuel Burer,et al.  A Two-Variable Approach to the Two-Trust-Region Subproblem , 2016, SIAM J. Optim..

[11]  José Mario Martínez,et al.  Local Minimizers of Quadratic Functions on Euclidean Balls and Spheres , 1994, SIAM J. Optim..

[12]  Ya-xiang,et al.  ON MAXIMA OF DUAL FUNCTION OF THE CDT SUBPROBLEM , 2001 .

[13]  Ya-Xiang Yuan,et al.  A trust region algorithm for equality constrained optimization , 1990, Math. Program..

[14]  Samuel Burer,et al.  The trust region subproblem with non-intersecting linear constraints , 2015, Math. Program..

[15]  Ya-Xiang Yuan,et al.  Recent advances in trust region algorithms , 2015, Mathematical Programming.

[16]  Ya-Xiang Yuan,et al.  Optimality Conditions for the Minimization of a Quadratic with Two Quadratic Constraints , 1997, SIAM J. Optim..

[17]  Alexander I. Barvinok.  Feasibility testing for systems of real quadratic equations , 1993, Discret. Comput. Geom..

[18]  Ya-Xiang Yuan,et al.  On Local Solutions of the Celis--Dennis--Tapia Subproblem , 1999, SIAM J. Optim..

[19]  Daniel Bienstock,et al.  A Note on Polynomial Solvability of the CDT Problem , 2014, SIAM J. Optim..

[20]  Yin Zhang,et al.  Computing a Celis-Dennis-Tapia trust-region step for equality constrained optimization , 1992, Math. Program..