Without loss of generality it is appropriate to consider a canonical hyperplane [ 8], where the parameters w, b are constrained by min i | < w, x i > + b | = 1.
The aim of constrained min-area retiming is to constrain the number of registers for a target clock period, under the assumption that all registers have the same area, the min-area retiming problem reduces to seeking a solution with the minimum number of registers in the circuit.
Therefore, the signal reconstruction problem can be described as the following constrained minimization problem, min x | | x | | 0 s.
Normally, the original image u ∈ R n will be found by solving the following constrained minimization problem: min u ∈ R n { J ( u ) : A u = f }, (1.2).
It is easy to verify that a solution to (10) also solves the following constrained minimization problem min x ∈ ℂ N x † R l x s.t.
The BIHT algorithms are developed for solving the following constrained optimization model min sumlimits_{i=1}^{m} h YPhi x)_{i}) quad text{s.t.} quad |x|_{0} le s quad text{and} quad |x|_{2}=1, (7).
In this paper, we are going to solve the following linearly constrained convex programming: min bigl{ f(x)|Ax=b, xinmathcal{R}^{n} bigr}, (1) where (f(x): mathcal{R}^{n}rightarrowmathcal{R}) is a closed proper convex function, (Ainmathcal{R}^{mtimes n}), (binmathcal{R}^{m}).
Motivated by the aforementioned models and the associated algorithms, we plan in this paper to reconstruct sparse signals from 1-bit measurements via solving the following constrained optimization model min |x|_{0} quad text{s.t.} quad YPhi x ge 0 quad text{and} quad |Phi x|_{1}=p, (9).
For the control of the blood glucose G with respect to the supply of parenteral and enteral nutrition as well as exogenous insulin we consider the following constrained minimization problem, min ( G, u ) ∈ Y × U J ( G, u ) subject to G = G ( u ) satisfying the ODE-system (1) and u ∈ U being the set of admissible controls.
Proposition 2.2 If we consider the constrained minimization problem min { f D ˜ g ( x ) ∣ x ∈ H 1 s.t. g ( x ) ∈ C }, its stationary point x ∗ ∈ H 1 satisfies { x ∗ ∈ H, g ( x ∗ ) ∈ C such that 〈 ∇ f D g ( x ∗ ), g ( x ) − g ( x ∗ ) 〉 ≥ 0, ∀ g ( x ) ∈ C, which is a general variational inequality involving a Lipschitz continuous and G-co-coercive operator.
For a constrained optimization problem min u ∈ K ⊂ U J ( u ), where J ( u ) is a convex functional on U and K is a convex subset of U, the iterative scheme reads ( n = 0, 1, 2, … ): { b ( u n + 1 2, v ) = b ( u n, v ) − ρ n ( J ′ ( u n ), v ), ∀ v ∈ U, u n + 1 = P K b ( u n + 1 2 ), (5.1).
