Based on our 269 cases dealing with fat injections into the breast, we considered these small cysts to be a minimal problem.
By virtue of the well-known Weierstrass theorem, there exists a point which is a minimal point of optimization problem (4.1).
By virtue of the well-know Weierstrass theorem, there exists a point which is a minimal point of optimization problem (4.1).
Assume that (hat{y}) is a minimal element of the following problem begin{aligned} min _{yin Y} {langle y^,yrangle +alpha Vert yVert }. end{aligned} (18) Then (hat{y}) is a properly efficient element of (1).
Then, there exist ((y^,alpha )in (mathbb {R}^{p}_)^{a#}) and (rin mathbb {R}^{p}) such that (hat{y}) is a minimal element of the following problem: begin{aligned} min _{yin Y} {langle y^,y-rrangle +alpha Vert y-rVert }. end{aligned} (19).
Then, there exists ((y^,alpha )in (mathbb {R}^{p}_)^{a#}) such that (hat{y}) is a minimal element of the following problem: begin{aligned} min _{yin Y} {langle y^,y-hat{y}rangle +alpha Vert y-hat{y}Vert }. end{aligned}.
If there exists F ∈ I N ( y ) such that ∥ F ∥ can be minimized, we say that the minimization of F is a problem subject to a minimal norm.
The minimal spanning tree problem is a popular problem of discrete optimization.
Mr. Gilbert added that proving identity with only minimal information is a problem, whatever form of communication is used to reach customer support.
