7 papers
Optimal Nonergodic Primal-Dual Complexity of Efficient Inexact Parameter-Free Augmented Lagrangian Methods
Arnesh Sujanani, Saeed Ghadimi, Henry Wołkowicz
Augmented Lagrangian (AL) methods are a classical framework for constrained optimization, but for directly verifiable approximate KKT points, known first-order complexity bounds fo…
Optimal Diagonal Preconditioning Beyond Worst-Case Conditioning: Theory and Practice of Omega Scaling
Saeed Ghadimi, Woosuk L. Jung, Arnesh Sujanani +2
We study optimal diagonal preconditioning using the classical worst-case -condition number and the averaging-based -condition number. For the -optimal preconditioning prob…
Finding Maximum Determinant Principal Submatrices via Hadamard Bounds and Projection Methods
Hao Hu, Stefan Sremac, Hugo J. Woerdeman +1
An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This…
A necessary condition for the guarantee of the superiorization method
Kay Barshad, Yair Censor, Walaa Moursi +2
We study a method that involves principally convex feasibility-seeking and makes secondary efforts of objective function value reduction. This is the well-known superiorization met…
On the local and global minimizers of the smooth stress function in Euclidean Distance Matrix problems
Mengmeng Song, Douglas Goncalves, Woosuk L. Jung +3
We consider the nonconvex minimization problem, with quartic objective function, that arises in the exact recovery of a configuration matrix of points when a Euc…
Projection, Degeneracy, and Singularity Degree for Spectrahedra
Haesol Im, Woosuk L. Jung, David Torregrosa-Belén +1
Facial reduction, FR, is a regularization technique for convex programs where the strict feasibility constraint qualification, CQ, fails.Though this CQ holds generically, failure i…