Abstract
In this paper, an unconstrained quadratic programming problem with uncertain parameters is discussed. For this purpose, the basic idea of optimizing the unconstrained quadratic programming problem is introduced. The solution method of solving linear equations could be applied to obtain the optimal solution for this kind of problem. Later, the theoretical work on the optimization of the unconstrained quadratic programming problem is presented. By this, the model parameters, which are unknown values, are considered. In this uncertain situation, it is assumed that these parameters are normally distributed; then, the simulation on these uncertain parameters are performed, so the quadratic programming problem without constraints could be solved iteratively by using the gradient-based optimization approach. For illustration, an example of this problem is studied. The computation procedure is expressed, and the result obtained shows the optimal solution in the uncertain environment. In conclusion, the unconstrained quadratic programming problem, which has uncertain parameters, could be solved successfully.
Highlights
Introduction illustrative example is further discusseda concluding remark is made.In nonlinear optimization, quadratic programming is the most simple optimization problem, and its applications have been widely studied [1], which are ranged from engineering [2, 3, 4] to business [5, 6, 7]
By the use of quadratic programming, this paper aims to discuss the uncertain parameters, which are presented in quadratic programming problem
B) Calculation Solution Procedure After the simulation is carried out to the uncertain parameters, the unconstrained quadratic programming problem is solved by using the optimization gradient approach [13, 15], which is given by x( = k +1) x(k ) + βk ⋅ ∇f (k )
Summary
Consider a general unconstrained quadratic programming problem [13, 14], given by Minimize f (x)= xTAx + bTx + c (1). To determine the optimal solution of the problem in (1), the first-order necessary condition [15, 16],. The analytical solution given by (4) would not exist if the parameters A, b, and c are unknown and incomplete information. From this point of view, a computational procedure is required to handle these uncertain parameters, so the unconstrained quadratic programming could be solved in practice. B) Calculation Solution Procedure After the simulation is carried out to the uncertain parameters, the unconstrained quadratic programming problem is solved by using the optimization gradient approach [13, 15], which is given by x( = k +1) x(k ) + βk ⋅ ∇f (k )
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