scholarly journals First-order differentiability properties of a class of equality constrained optimal value functions with applications

2020 ◽  
Author(s):  
Kevin Sturm
Keyword(s):  
Sufficient Conditions ◽  
Quadratic Function ◽  
Equality Constraints ◽  
Shape Optimisation ◽  
Infinitely Many Solutions ◽  
Value Functions ◽  
Finite Dimensional ◽  
Optimal Value ◽  
Adjoint Approach ◽  
The Right

In this paper we study the right differentiability of a parametric infimum function over a parametric set defined by equality constraints. We present a new theorem with sufficient conditions for the right differentiability with respect to the parameter. Target applications are nonconvex objective functions with equality constraints arising in optimal control and shape optimisation. The theorem makes use of the averaged adjoint approach in conjunction with the variational approach of Kunisch, Ito and Peichl. We provide two examples of our abstract result: (a) a shape optimisation problem involving a semilinear partial differential equation which exhibits infinitely many solutions, (b) a finite dimensional quadratic function subject to a nonlinear equation.

Dynamic admission control for loss systems with batch arrivals

2005 ◽  
Vol 37 (04) ◽  
pp. 915-937 ◽  
Author(s):  
E. L. Örmeci ◽  
A. Burnetas
Keyword(s):  
Admission Control ◽  
Sufficient Conditions ◽  
Monotonicity Property ◽  
Value Functions ◽  
Single Class ◽  
Batch Arrivals ◽  
Optimal Value ◽  
Service Rates ◽  
Definition Of ◽  
Optimal Value Functions

We consider the problem of dynamic admission control in a Markovian loss system with two classes. Jobs arrive at the system in batches; each admitted job requires different service rates and brings different revenues depending on its class. We introduce the definition of a ‘preferred class’ for systems receiving mixed and single-class batches separately, and derive sufficient conditions for each system to have a preferred class. We also establish a monotonicity property of the optimal value functions, which reduces the number of possibly optimal actions.

scholarly journals Finite-dimensional approximations for Nica–Pimsner algebras

2019 ◽  
Vol 40 (12) ◽  
pp. 3375-3402
Author(s):  
EVGENIOS T. A. KAKARIADIS
Keyword(s):  
Sufficient Conditions ◽  
Graph Products ◽  
Product Systems ◽  
Finite Dimensional ◽  
Ordered Groups ◽  
Lattice Ordered Groups ◽  
Abelian Lattice ◽  
Fixed Point Algebra ◽  
The Right ◽  
Necessary And Sufficient

We give necessary and sufficient conditions for nuclearity of Cuntz–Nica–Pimsner algebras for a variety of quasi-lattice ordered groups. First we deal with the free abelian lattice case. We use this as a stepping-stone to tackle product systems over quasi-lattices that are controlled by the free abelian lattice and satisfy a minimality property. Our setting accommodates examples like the Baumslag–Solitar lattice for $n=m>0$ and the right-angled Artin groups. More generally, the class of quasi-lattices for which our results apply is closed under taking semi-direct and graph products. In the process we accomplish more. Our arguments tackle Nica–Pimsner algebras that admit a faithful conditional expectation on a small fixed point algebra and a faithful copy of the coefficient algebra. This is the case for CNP-relative quotients in-between the Toeplitz–Nica–Pimsner algebra and the Cuntz–Nica–Pimsner algebra. We complete this study with the relevant results on exactness.

scholarly journals Dynamic admission control for loss systems with batch arrivals

2005 ◽  
Vol 37 (4) ◽  
pp. 915-937 ◽  
Author(s):  
E. L. Örmeci ◽  
A. Burnetas
Keyword(s):  
Admission Control ◽  
Sufficient Conditions ◽  
Monotonicity Property ◽  
Value Functions ◽  
Single Class ◽  
Batch Arrivals ◽  
Optimal Value ◽  
Service Rates ◽  
Definition Of ◽  
Optimal Value Functions

We consider the problem of dynamic admission control in a Markovian loss system with two classes. Jobs arrive at the system in batches; each admitted job requires different service rates and brings different revenues depending on its class. We introduce the definition of a ‘preferred class’ for systems receiving mixed and single-class batches separately, and derive sufficient conditions for each system to have a preferred class. We also establish a monotonicity property of the optimal value functions, which reduces the number of possibly optimal actions.

scholarly journals Stability Analysis of a Class of Higher Order Difference Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Yuanyuan Liu ◽  
Fanwei Meng
Keyword(s):  
Difference Equations ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Nonlinear Difference Equations ◽  
Order Difference ◽  
Finite Dimensional ◽  
Infinite Delays ◽  
Stability And Instability ◽  
The Stability ◽  
The Right

We consider the sufficient conditions for asymptotic stability and instability of certain higher order nonlinear difference equations with infinite delays in finite-dimensional spaces. With the aid of the general comparison condition on the right-hand side functionfk(·), we generalize the stability and instability result.

scholarly journals Potential Operators on Cones of Nonincreasing Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Alexander Meskhi ◽  
Ghulam Murtaza
Keyword(s):  
Mixed Type ◽  
Sufficient Conditions ◽  
Product Type ◽  
Necessary And Sufficient Conditions ◽  
Lebesgue Spaces ◽  
Potential Operators ◽  
Right Hand ◽  
The Right ◽  
Necessary And Sufficient

Necessary and sufficient conditions on weight pairs guaranteeing the two-weight inequalities for the potential operators(Iαf)(x)=∫0∞(f(t)/|x−t|1−α)dtand(ℐα1,α2f)(x,y)=∫0∞∫0∞(f(t,τ)/|x−t|1−α1|y−τ|1−α2)dtdτon the cone of nonincreasing functions are derived. In the case ofℐα1,α2, we assume that the right-hand side weight is of product type. The same problem for other mixed-type double potential operators is also studied. Exponents of the Lebesgue spaces are assumed to be between 1 and ∞.

Nonholonomic deformation of coupled and supersymmetric KdV equations and Euler–Poincaré–Suslov method

2015 ◽  
Vol 27 (04) ◽  
pp. 1550011 ◽  
Author(s):  
Partha Guha
Keyword(s):  
Kdv Equation ◽  
Infinite Dimensional ◽  
Kdv Equations ◽  
Finite Dimensional ◽  
Euler Top ◽  
Two Component ◽  
Finite Dimensional Case ◽  
Coupled Kdv Equations ◽  
The Right ◽  
Supersymmetric Kdv Equation

Recently, Kupershmidt [38] presented a Lie algebraic derivation of a new sixth-order wave equation, which was proposed by Karasu-Kalkani et al. [31]. In this paper, we demonstrate that Kupershmidt's method can be interpreted as an infinite-dimensional analogue of the Euler–Poincaré–Suslov (EPS) formulation. In a finite-dimensional case, we modify Kupershmidt's deformation of the Euler top equation to obtain the standard EPS construction on SO(3). We extend Kupershmidt's infinite-dimensional construction to construct a nonholonomic deformation of a wide class of coupled KdV equations, where all these equations follow from the Euler–Poincaré–Suslov flows of the right invariant L2 metric on the semidirect product group [Formula: see text], where Diff (S1) is the group of orientation preserving diffeomorphisms on a circle. We generalize our construction to the two-component Camassa–Holm equation. We also give a derivation of a nonholonomic deformation of the N = 1 supersymmetric KdV equation, dubbed as sKdV6 equation and this method can be interpreted as an infinite-dimensional supersymmetric analogue of the Euler–Poincaré–Suslov (EPS) method.

Unknown input fractional-order functional observer design for one-side Lipschitz time-delay fractional-order systems

2019 ◽  
Vol 41 (15) ◽  
pp. 4311-4321 ◽  
Author(s):  
Mai Viet Thuan ◽  
Dinh Cong Huong ◽  
Nguyen Huu Sau ◽  
Quan Thai Ha
Keyword(s):  
Time Delay ◽  
Nonlinear Systems ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Quadratic Function ◽  
Observer Design ◽  
Linear Matrix ◽  
Unknown Input ◽  
Functional Observer ◽  
The One

This paper addresses the problem of unknown input fractional-order functional state observer design for a class of fractional-order time-delay nonlinear systems. The nonlinearities consist of two parts where one part is assumed to satisfy both the one-sided Lipschitz condition and the quadratically inner-bounded condition and the other is not necessary to be Lipschitz and can be regarded as an unknown input, making the wider class of considered nonlinear systems. By taking the advantages of recent results on Caputo fractional derivative of a quadratic function, we derive new sufficient conditions with the form of linear matrix inequalities (LMIs) to guarantee the asymptotic stability of the systems. Four examples are also provided to show the effectiveness and applicability of the proposed method.

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