A tutorial on geometric programming
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Citations
Unified Framework to Regularized Covariance Estimation in Scaled Gaussian Models
Interconnect-Based Design Methodologies for Three-Dimensional Integrated Circuits : Vertical integration is a novel communications paradigm where interconnect design is a primary focus
Application of geometric programming to transformer design
Power Control for Cognitive Radio Networks Under Channel Uncertainty
First-order Methods for Geodesically Convex Optimization
References
Convex Optimization
Numerical Optimization
Linear and nonlinear programming
Related Papers (5)
Frequently Asked Questions (14)
Q2. What is the main trick to solving a GP efficiently?
The main trick to solving a GP efficiently is to convert it to a nonlinear but convex optimization problem, i.e., a problem with convex objective and inequality constraint functions, and linear equality constraints.
Q3. What is the way to fit a model to a monomial?
One useful extension of monomial fitting is to include a constant offset, i.e., to fit the data (x(i), f (i)) to a model of the formf (x) = b + cxa11 · · ·xann ,where b ≥ 0 is another model parameter.
Q4. What are the posynomial functions of the wire segment widths wi?
The wire segment resistance and capacitance are both posynomial functions of the wire widths wi , which will be their design variables.
Q5. What is the common method for finding the trade-off curve of the objective and one or?
Another common method for finding the trade-off curve (or surface) of the objective and one or more constraints is the weighted sum method.
Q6. What is the constraint that the truss should be strong enough to carry the load?
The constraint that the truss should be strong enough to carry the load F1 means that the stress caused by the external force F1 must not exceed a given maximum value.
Q7. What are the applications of geometric programming in other fields?
Applications of geometric programming in other fields include:• Chemical engineering (Clasen 1984; Salomone and Iribarren 1993; Salomone et al.
Q8. How did the authors find the posynomial approximations for the same number?
The authors illustrate posynomial fitting using the same data points as those used in the max-monomial fitting example given in Sect. 8.4. The authors used a Gauss-Newton method to find K-term posynomial approximations, ĥK(x), for K = 3, 5, 7, which (locally, at least) minimize the sum of the squares of the relative errors.
Q9. How do the authors find the optimal trade-off curve?
The optimal trade-off curve (or surface) can be found by solving the perturbed GP (12) for many values of the parameter (or parameters) to be varied.
Q10. How can the authors handle a generalized posynomial with a negative coefficient?
This analysis suggests that the authors can handle composition of a generalized posynomial with any function whose series expansion has no negative coefficients, at least approximately, by truncating the series.
Q11. What is the definition of a nonlinear least-squares problem?
This is a nonlinear least-squares problem, which can be solved (usually) using methods such as the Gauss-Newton method (Bertsekas 1999; Luenberger 1984; Nocedal and Wright 1999).
Q12. What is the problem of finding a local monomial approximation of a?
8.2 Local monomial approximationThe authors consider the problem of finding a monomial approximation of a differentiable positive function f near a point x (with xi > 0).
Q13. What is the method for the case with only one generalized posynomial equality?
The authors first describe the method for the case with only one generalized posynomial equality constraint (since it is readily generalizes to the case of multiple generalized posynomial equality constraints).
Q14. what is the converse for generalized posynomials?
The interesting part here is the converse for generalized posynomials, i.e., the observation that if F can be approximated by a convex function, then f can be approximated by a generalized posynomial.