Ebrahim Sarabi
Miami University-Oxford, OH·Mathematics & Statistics
Many practical computing tasks come down to finding the best possible option among many: fitting a model to noisy data, representing a signal with as few components as possible, cleaning up an image, or deciding where to place sensors. These are optimization problems, and two questions matter for them.
- Fields
Mathematics & Statistics
Computer Science
- Topics
optimization
variational analysis
second subderivative
- Grants
- 1 known grant, through Jul 2027
What they work on
- Establish parabolic regularity and twice epi-differentiability for piecewise linear-quadratic composite problems and classes of matrix optimization problems, extending second-order calculus to objectives that are not differentiable in the usual sense.
- Study the twice epi-differentiability of augmented Lagrangians associated with composite optimization problems and characterize their quadratic growth condition through the second-order sufficient condition.
- Analyze stability of composite optimization problems, including strong metric regularity, strong metric subregularity and non-criticality of Lagrange multipliers, the quantities that measure how constraints bind at a solution.
- Carry out local and global convergence analysis of the augmented Lagrangian method for composite problems, focusing on cases where Lagrange multipliers are not unique, using the second subderivative as the main tool.
More about the research
First, how do the best solutions behave when the problem's data is perturbed slightly, as real data always is? Second, can algorithms find those solutions efficiently? The difficulty is that many of these problems involve functions with kinks or breaks, so the usual calculus of derivatives does not apply directly.
Why it matters
Optimization problems of this kind underlie regression models, sparse representation of signals, image processing and sensor placement. Clearer second-order theory tells practitioners when a computed solution is stable under perturbed data and how quickly standard algorithms such as the augmented Lagrangian method will converge, including the hard case of non-unique Lagrange multipliers, which could lead to more reliable and faster numerical methods for these applications.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Frank Curtis
Lehigh University, PA·Mathematics & Statistics
Revisit the basic properties that gradient sampling methods rely on to guarantee convergence, and strengthen them for nonconvex, nonsmooth, locally Lipschitz problems whose function values are corrupted by computational noise.
Adrian Lewis
Cornell University, NY·Mathematics & Statistics
Extend Łojasiewicz-type rescaling techniques to analyze the complexity of first-order and active-set algorithms on semi-algebraic problems in hyperbolic, non-Euclidean and infinite-dimensional spaces.
Andrei Draganescu
University of Maryland-Baltimore County, MD·Mathematics & Statistics
Develop low-rank gradient flow (LRGF), a first-order optimization method that builds quadratic approximations with low-rank Hessians and computes their gradient flow exactly, ending each step with a Wolfe-condition line search.
The school
Miami University-Oxford: 5 labs on PI Pages, $29M a year on research, 71 research doctorates a year.
Reach out
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