In Step 1, as problem (7) is a nonlinear, nonconvex programming problem with a linear objective function.
Sufficient conditions to achieve the consensus with guaranteed cost are presented and expressed as a continuous constrained optimization problem with a linear objective function, linear and bilinear matrix inequalities constraints, involving the co-design of the controller gain matrix and event triggering parameters.
The basic idea of the LMI is to approximate a given input/output modeling problem posed as a quadratic optimization problem with a linear objective and so-called LMI constraint [ 8].
As a subfield of convex optimization, SDP concerns with the optimization of a linear objective function to be maximized or minimized over the intersection of the cone of positive semi-definite matrices with an affine space, i.e., a spectrahedron [11].
Integer programming, in particular, integer linear programming (ILP) is to maximize (or minimize) a linear objective function with linear constraints (i.e., linear inequalities and linear equations) with all the variables taking integer values.
By dropping the rank-one constraint, problem (34) becomes a convex semidefinite program (SDP) for a given α that consists of a linear objective function together with a set of LMI constraints, which can thus be solved effectively via standard convex optimization techniques such as the interior point method [35].
This SOCP includes a linear objective function and a set of linear and conic constraints.
The final model has a linear objective function and a set of non-linear constraints.
This was expected, considering that the system is studied at the complete organ level, involving competing processes which can rarely be modeled with a single linear objective function.
This paper develops an efficient algorithm to solve a mathematical programming problem with a linear fractional objective function that models changing DM preferences and linear constraints.
Then the actual dense realization can be determined by solving the following LP feasibility problem for A k (with arbitrary linear objective function): (12) Y ⋅ A k = M, ∑ i = 1 m [ A k ] i, j = 0, j = 1, …, m, ε i j ≤ [ A k ] i, j ≤ U i j, i, j = 1, …, m, i ≠ j, [ A k ] i, i ≤ 0, i = 1, …, m.
