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- And coderivatives (1)
- Asplund generated space (1)
- Bolza problem (1)
- Difference-type functions (1)
- Differential inclusions (1)
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- Discrete approximations (1)
- Frechet normals (1)
- Geometric and operator constraints (1)
- Infinite dimension (1)
- Limiting Frechet normal cone (1)
- Limiting Frechet subdifferential (1)
- Mean value theorem. (1)
- Necessary optimality conditions (1)
- Nonsmooth analysis (1)
- Optimal control (1)
- Relaxation stability (1)
- Subdifferential calculus (1)
- Subgradients (1)
- Sum rule (1)
- Value and strong solution convergences (1)
- Variational analysis and constrained optimization (1)
- Weak sharp minima (1)
Articles 1 - 3 of 3
Full-Text Articles in Applied Mathematics
Discrete Approximations Of Differential Inclusions In Infinite-Dimensional Spaces, Boris S. Mordukhovich
Discrete Approximations Of Differential Inclusions In Infinite-Dimensional Spaces, Boris S. Mordukhovich
Mathematics Research Reports
In this paper we study discrete approximations of continuous-time evolution systems governed by differential inclusions with nonconvex compact values in infinite-dimensional spaces. Our crucial result ensures the possibility of a strong Sobolev space approximation of every feasible solution to the continuous-time inclusion by its discrete-time counterparts extended as Euler's "broken lines." This result allows us to establish the value and strong solution convergences of discrete approximations of the Bolza problem for constrained infinite-dimensional differential/evolution inclusions under natural assumptions on the initial data.
Subdifferential Calculus In Asplund Generated Spaces, Marian Fabian, Philip D. Loewen, Boris S. Mordukhovich
Subdifferential Calculus In Asplund Generated Spaces, Marian Fabian, Philip D. Loewen, Boris S. Mordukhovich
Mathematics Research Reports
We extend the definition of the limiting Frechet subdifferential and the limiting Frechet normal cone from Asplund spaces to Asplund generated spaces. Then we prove a sum rule, a mean value theorem, and other statements for this concept.
Fréchet Subdifferential Calculus And Optimality Conditions In Nondifferentiable Programming, Boris S. Mordukhovich, Nguyen Mau Nam, N. D. Yen
Fréchet Subdifferential Calculus And Optimality Conditions In Nondifferentiable Programming, Boris S. Mordukhovich, Nguyen Mau Nam, N. D. Yen
Mathematics Research Reports
We develop various (exact) calculus rules for Frechet lower and upper subgradients of extended-realvalued functions in general Banach spaces. Then we apply this calculus to derive new necessary optimality conditions for some remarkable classes of problems in constrained optimization including minimization problems for difference-type functions under geometric and operator constraints as well as subdifferential optimality conditions for the so-called weak sharp minima.