The phrase "as optimal solution" is not correct in English; it should be "as an optimal solution." You can use it when discussing the best possible answer or approach to a problem in a specific context.
Example: "In this scenario, we have identified the strategy as an optimal solution for maximizing efficiency."
Alternatives: "as the best solution" or "as the ideal solution."
Many heuristics have been developed for this problem, as well as optimal solution methods which are applicable only to small instances.
Technical relationships among them are used to systematize optimal values of design and operative variables of a CCGT power plant into optimal solution sets, named here as optimal solution families.
We return as optimal solution the one that leads to the minimal penalty at depth h.
Here the main question arises: can we accept the matrix homothety ({mathbf{X}} = k{mathbf{A}}) as optimal solution for proportionality case of a general matrix-updating problem?
Here the question arises: can we accept the initial matrix homothety as optimal solution for proportionality case of matrix-updating problem?
It means that, from viewpoint of the Kullback Leibler divergence minimization approach, the matrix homothety ({mathbf{X}} = k{mathbf{A}}) can be classified as optimal solution for proportionality case of a general matrix-updating problem.
Some studies support the view that governance structures endogenously arise as optimal solutions to the contracting environment of the firm.
In addition, retrofit schemes to differentiate the retrofit level according to the retrofit position are proposed as optimal solutions.
In contrast to other generalized regression techniques that approximate conditional superquantiles by various combinations of conditional quantiles, we directly and in perfect analog to classical regression obtain superquantile regression functions as optimal solutions of certain error minimization problems.
In this note we give a property of the optimal solutions to the spectral commutant lifting theorem of H. Bercovici, C. Foias, and A. Tannenbaum (Trans. Amer. Math. Soc., in press) which shows that such solutions are spectral analogues of inner functions which appear as optimal solutions in classical dilation theory.
Comparative results in Table 5 indicate that, according to the CAPEX, both scenarios I and II as optimal solutions in this paper would save about 24.3% and 17.7%, respectively, compared to scenario III.
