scholarly journals Technical Note—Optimality Conditions and Recession Cones

1975 ◽  
Vol 23 (3) ◽  
pp. 549-553 ◽  
Author(s):  
Robert A. Abrams ◽  
Adi Ben-Israel
Keyword(s):  
Optimality Conditions ◽  
Technical Note ◽  
Recession Cones

New AAC Access Strategy for Gesture Tracking: A Technical Note

2012 ◽  
Vol 21 (1) ◽  
pp. 11-16 ◽  
Author(s):  
Susan Fager ◽  
Tom Jakobs ◽  
David Beukelman ◽  
Tricia Ternus ◽  
Haylee Schley
Keyword(s):  
Augmentative And Alternative Communication ◽  
Technical Note ◽  
Head Tracking ◽  
Alternative Communication ◽  
Access Methods ◽  
Cord Injury ◽  
Physical Limitations ◽  
Gesture Tracking ◽  
Communication Needs ◽  
Tracking Device

Abstract This article summarizes the design and evaluation of a new augmentative and alternative communication (AAC) interface strategy for people with complex communication needs and severe physical limitations. This strategy combines typing, gesture recognition, and word prediction to input text into AAC software using touchscreen or head movement tracking access methods. Eight individuals with movement limitations due to spinal cord injury, amyotrophic lateral sclerosis, polio, and Guillain Barre syndrome participated in the evaluation of the prototype technology using a head-tracking device. Fourteen typical individuals participated in the evaluation of the prototype using a touchscreen.

Technical Note

1998 ◽  
Vol 47 (3) ◽  
pp. 153-160
Author(s):  
Wang ◽  
Park ◽  
Kang ◽  
Oh
Keyword(s):  
Technical Note

Optimal control of higher order differential inclusions with functional constraints

2020 ◽  
Vol 26 ◽  
pp. 37 ◽  
Author(s):  
Elimhan N. Mahmudov
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Higher Order ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Functional Constraints ◽  
Complementary Slackness ◽  
Complementary Slackness Conditions

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler–Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

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