A strongly convex function of simple structure (for example, separable) is minimized under affine constraints. A dual problem is constructed and solved by applying a fast gradient method. The necessary properties of this method are established relying on which, under rather general conditions, the ...
In this paper we use basic properties of strongly convex functions to obtain new inequalities including Jensen's type and Jensen-Mercer type inequalities. Applications for special means are pointed out as well. We also give a Jensen's operator inequality for strongly convex functions. As a corolla...
y_1<y_2<\cdots <y_n, and z_i=f(y_i), i\in [n], where f is a strictly convex function.An example with n=5 is illustrated in the picture (where z_i=y_i^2 and y_i=-y_{6-i}). Hereinafter, we think of x, y, z as “vertical,”“left-to-right,” and “to-depth...
On a fixed time interval we consider zero-sum nonlinear differential games for which the integrand in the criterion functional is a sufficiently strongly convex-concave function of chosen controls. It is shown that in our setting there exists a saddle point in the class of programmed strategies, ...
fixed nonsmooth functionThis paper presents an algorithmic solution, the adaptive projected subgradient method, to the problem of asymptotically minimizing a certain sequence of non-negative continuous convex functions over the fixed point set of a strongly attracting nonexpansive mapping in a real Hilbert...
F:[0,T]×K→L2([0,T],Rq), where K is a convex subset of R+q, is said to be: • hemicontinuous in the sense of Fan (briefly F-hemicontinuous) if and only if for all v∈L2([0,T],R+q) the function u→∫0T〈F(t,u(t)),u(t)-v(t)〉dtis lower semicontinuous on...
The inference relation induced by a ranking function κ is defined by(1) Note that the condition κ(A)=∞ in (1) ensures that system P's axiom (REF): is satisfied also for A≡⊥, i.e., ensuring that . In the next section, we will consider operators that map belief bases to ...
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Example 2.5 For T=(n1,n2,n3,n4) and ω={3}, the Λ(T)ω matrix is (n1n2n3n4000100010001000100001001). Theorem 2.6 [17, Theorem 3.7] The set ω is a face of the strongly robust complex ΔT if and only if IΛ(T)ω is strongly robust. 3 On the dimension of the strongly robust...
The purpose of this paper is to introduce the spaces of sequences that are strongly almost (ω, λ, q)-summable with respect to a modulus function. We give some relations related to these sequence spaces. It is also shown that if a sequence is strongly (