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Application of numerical algebraic geometry in parametric semidefinite programming
Tingting Tang
San Diego State University
Abstract:
In this talk, we study the property of the solution of semidefinite programs with multi-dimensional perturbation variables using the Davidenko differential equations. Under the assumptions of strict complementary and non-degeneracy, we aim to find the a priori unknown maximal convex permissible perturbation set where the semidefinite program has a unique optimum and the optimum is analytic. A sweeping Euler numerical method is developed to approximate this a priori unknown perturbation set and solve the semidefinite program within this set. We prove local and global error bounds for this second-order sweeping Euler scheme and demonstrate results on several examples.
Tuesday, May 18, 2021
11:00AM Zoom ID 939 3177 8552
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Randolph E. Bank
Philip E. Gill
Michael Holst
Administrative Contact:
[ Click to Send Email ]
Tingting Tang
San Diego State University
Abstract:
In this talk, we study the property of the solution of semidefinite programs with multi-dimensional perturbation variables using the Davidenko differential equations. Under the assumptions of strict complementary and non-degeneracy, we aim to find the a priori unknown maximal convex permissible perturbation set where the semidefinite program has a unique optimum and the optimum is analytic. A sweeping Euler numerical method is developed to approximate this a priori unknown perturbation set and solve the semidefinite program within this set. We prove local and global error bounds for this second-order sweeping Euler scheme and demonstrate results on several examples.
Tuesday, May 18, 2021
11:00AM Zoom ID 939 3177 8552