| Abstract: |
| I will present a general framework for estimating constraint violations in projection-free iterative methods for minimizing energy functionals subject to pointwise constraints, which are non-convex and involve operator quadratic in the function and/or its derivatives. Our analysis proves to be universal to all projection-free methods that utilize tangent space update strategy. We show that the constraint error bounds are determined solely by the sum of finite differences (of various orders) of the iterates, which reflect (pseudo-)temporal regularities of their continuous counterparts. A new class of projection-free BDF-k second-order-flow methods are proposed achieving modified energy stability and ensuring higher order conditional/unconditional constraint consistency than existing projection-free gradient flow methods. |
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