Sentence examples for minimization by introducing from inspiring English sources

Patients are randomly assigned, in a 1 1 ratio, to either an observation group or UFT adjuvant therapy group, using minimization by introducing a random element with a 0.8 assignment probability [ 14], balanced on the following stratification factors: depth of tumor invasion (T3 vs. T4), number of lymph-nodes examined (<12 vs. ≥12) and institution.

We can also cast it as a minimization problem by introducing gap functions [1].

Our purpose of the present manuscript is to study the more general case of the proximal split minimization problems by introducing new algorithms with the regularization technique.

By introducing a convex minimization problem, the split feasibility problem (SFP) is equivalent to a variational inequality problem (VIP), which involves a Lipschitz continuous and inversely strong monotone (ism) operator, see [14 22].

By introducing orthonormal constraints in the minimization functionals equation (12) leads to the unconstrained minimization of, E I = E 0 I + β ∫ Ω I I c γ d x → (15).

In addition, rank minimization problems (RMPs) are introduced and equivalently transformed into RCOPs by introducing a quadratic matrix equality constraint.

The problem of functional minimization is reduced to construction of a sequence of smooth nonlinear programming problems by introducing the auxiliary variables and applying the augmented Lagrangian method.

Equation (4) is transformed to the following l1-norm minimization problem: and then converted to the standard primal and dual forms in linear programming: By introducing a logarithmic barrier term, (P) is converted to the following logarithmic barrier problems: where θ is the barrier parameter.

In order to avoid CFL condition, researchers in [36] proposed completely augmented Lagrangian method by introducing eight auxiliary variables and four penalty parameters, leading to numerous sub-minimization and sub-maximization problems for every introduced variable.

By introducing the concept of perfect S-IDNC solution, we proved the NP-hardness of APDD minimization.

By introducing the Lagrangian function, SQP solves a series of quadratic programming sub-problems, each involving the minimization of a quadratic approximation of the objective function subject to a linear approximation of the constraints.