Computationally, the problem can be represented as a graph problem.
With the aid of certain fundamental concepts of mathematics, Fourier series expansion, and metaheuristic methods, ODEs can be represented as an optimization problem.
Identification of minimal reaction set can be represented as an optimization problem given by [ 16]: (2) minimize z = ∑ j = 1 M y j s. t ∑ j = 1 M S ij v j = 0 i = 1, 2, …, N v j min · y j ≤ v j ≤ v j max · y j j = 1, 2, …, M y j ∈ 0, 1 j = 1, 2, …, M v biomass ≥ v biomass max v j ∈ R Here, v j min and v j max represent the lower and upper bounds for the flux through reaction j.
The system above can be represented as a fixed point problem of the form (1.11).
A monotonic increasing or decreasing membership function is used to define the degree of satisfaction for each objective function so that the fuzzy goal optimization problem is then represented as an augmented minimax problem formulated as mixed-integer nonlinear programming (MINLP) models.
In this paper, a new iterative approach to probabilistic robust controller design is presented, which is applicable to any robust controller/filter design problem that can be represented as an LMI feasibility problem.
To wit: A problem represented as a Boolean formula with 10 variables that affords a linear solution taking one hundredth of a second to complete would take just four hundredths and six hundredths of a second to complete if the formula had instead 40 and 60 variables respectively.
The set of test patterns is implicitly represented as a Boolean formula satisfiability problem in CNF, like in common SAT-based ATPGs.
According to [19], (9) can be represented as a solution to the problem min R S, t η 2 t s. t.
For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem.
