Representation Theorems for Indefinite Quadratic Forms Revisited

The TAN $2Θ$ Theorem for Indefinite Quadratic Forms

A version of the Davis-Kahan Tan $2Θ$ theorem [SIAM J. Numer. Anal. \textbf{7} (1970), 1 -- 46] for not necessarily semibounded linear operators defined by quadratic forms is proven. This theorem generalizes a recent result by Motovilov and Selin [Integr. Equat. Oper. Theory \textbf{56} (2006), 511 -- 542].

Representation Theorems for indefinite quadratic forms without spectral gap

The First and Second Representation Theorem for sign-indefinite quadratic forms are extended. We include new cases of unbounded forms associated with operators that do not necessarily have a spectral gap around zero. The kernel of the associated operators is determined for special cases. This extends results by Grubišić, Kostrykin, Makarov and Veselić in [Mathematika 59 (2013), 169--189].

Indefinite least squares with a quadratic constraint

An abstract indefinite least squares problem with a quadratic constraint is considered. This is a quadratic programming problem with one quadratic equality constraint, where neither the objective nor the constraint are convex functions. Necessary and sufficient conditions are found for the existence of solutions.

Regularization of an Indefinite Abstract Interpolation Problem with a Quadratic Constraint

Along this work we study an indefinite abstract smoothing problem. After establishing necessary and sufficient conditions for the existence of solutions to this problem, the set of admissible parameters is discussed in detail. Then, its relationship with a linearly constrained interpolation problem is analyzed.

无限维耗散系统的最优控制

Optimal control of infinite-dimensional dissipative systems

研究无限维耗散系统线性二次最优控制问题，证明不定成本函数问题等价于非负成本函数问题，并建立值函数关系及Lur'e方程。