Sentence examples for problem under which from inspiring English sources

In the same reference, the authors left an open problem: under which conditions does (1.5) hold?

We propose a generalized Guignard constraint qualification and a generalized Abadie constraint qualification for this problem under which necessary optimality conditions are proved.

In this paper we deal mostly with the following problem: under which conditions a family of algebras ({mathcal{A}_{lambda }}_{lambda in Lambda }) has a full set of lacunae.

By applying a model predictive control (MPC) method, we formulate the problem of finding the optimal joint train regulation and passenger flow control strategy as the problem of solving a set of quadratic programming (QP) problems, under which an optimal control law can be numerically calculated efficiently using a quadratic programming algorithm.

An analysis of the problem headings under which emollient prescriptions were issued was carried out for the 121 practices using problem headings satisfactorily.

Lastly, in Section 4, we compare the spectrum of the original boundary value problem with that of the transformed boundary value problem and show under which conditions the transformed boundary value problem has one more eigenvalue, one less eigenvalue, or the same number of eigenvalues as the original boundary value problem.

Next, we will point out two special cases, under which problem (7) is equivalent to problem (5) or, equivalently, any optimal solution to (7) is achieved with constraint (7a) active.

Huang et al. ([1994b]) proposed an interval fuzzy quadratic programming (IFQP) approach for optimization analysis of waste management problems under uncertainty, which integrates interval-parameter programming, fuzzy linear programming and fuzzy quadratic programming within a general optimization framework.

The grey-based PROMETHEE II methodology is designed to represent and analyze decision problems under uncertainty, which are characterized by limited input data and uncertain preferences of Decision Makers (DMs).

However, it is shown to be possible to avoid some of the need for dealing with these nonlinear problems by identifying conditions under which they can be replaced by linear problems.

The problem is the regime under which both have risen to prominence.