As a result, the limit state function is reformulated as a function of only random variables and time.
Then, the inaccessibility minimizing, i.e., accessibility maximizing, objective function is reformulated as an integrated optimization problem for joint locating parking lots and corresponding parking space capacity.
In this paper, to overcome the above mentioned problems the design procedure is reformulated as a set of cost functions and constraints.
The single objective function was converted into two objective functions for minimizing the mean and variation while the constraint functions were reformulated with the acceptable robustness level.
Difference-of-convex-functions programming (DCP [40] is a widely applicable approach in global optimization where non-convex objective and constraint functions are reformulated as the difference of convex functions, cf.[37, 38] for recent applications in power control.
(4) Minimize w, b, ξ, ξ * 1 2 w 2 + C ∑ i = 1 n (ξ i + ξ i * ) Subject to: (5) y i - w, x i - b ≤ ε + ξ i w, x i + b - y i ≤ ε + ξ i * ε, ξ i, ξ i * ≥ 0 If the space of the original data doesn't have a linear relationship with the dependent variable, the function f is reformulated from the primal model to the dual model Expression 6).
This problem is known to be an NP-hard problem [ 62], although it can be reduced to a polynomially solvable problem if the cost function in Equation 3 is reformulated as an additive objective function [ 62].
Using parameter-dependent Lyapunov functions, the control design is reformulated as a parameter-dependent LMI optimization with a single line search parameter.
Based on the smoothed Fischer-Burmeister function, the variational inequality problem is reformulated as a system of parameterized smooth equations.
Based on a perturbed smoothing function, the underlying system of inequalities is reformulated as a system of smooth equations, and a smoothing-type method is proposed to solve it iteratively so that a solution of the system of inequalities is found.
In addition, the simulation-optimization program is reformulated using a penalty function, resulting in less optimization variables and better convergence of the simulation program.
