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This condition is given in terms of a system of linear matrix inequalities with rank constraints, and can be solved using some existing algorithms.
The transformed problem is one of targeting under constraints and can be solved iteratively by combining pinch analysis algorithm with evaporator simulator.
Furthermore, by an SOS-based method the existence of the proposed controller is given in terms of the solvability of polynomial matrix inequalities (PMIs), which are formulated as SOS constraints and can be solved by the recently developed SOS solvers.
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This design can be transformed into an extended diagonal loading problem, whose loading factor is directly related to the SF constraint and can be solved by the existing numerical methods.
Although the new problem is still nonlinear on the boundary, this problem no longer has the inequality constraint and can be solved by the semismooth Newton method with local superlinear convergence rate [7, 14].
This is a constraint optimization problem and can be solved using the Lagrangian multiplier method.
Together with other conventional constraints, an optimization model is then set up and can be solved by Genetic Algorithm (GA).
For triangulation graphs, the proposed optimization problem is a linear least-squares problem with linear constraints and thus can be solved using standard methods.
For a fixed FEC-based MDC, we show how this optimization can be approximated by a convex optimization problem with linear constraints, and thus, can be solved efficiently.
From (18),we can observe that the optimization problem (10) that involves the two constraints (Vert boldsymbol {w}^{T}_{x}boldsymbol {X}Vert _{2}=1) and (Vert boldsymbol {w}^{T}_{y}boldsymbol {Y}Vert _{2}=1) has now been transformed into a rank-1 matrix approximation problem free of constraints and which can be solved with an SVD.
Posynomial models are widely used in various engineering design endeavors, such as circuits, aerospace and structural design, mainly due to the fact that design problems cast in terms of posynomial objectives and constraints can be solved efficiently by means of a convex optimization technique known as geometric programming (GP).
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