Effectiveness of a geometric programming algorithm for optimization of machining economics models
Computers and Operations Research
An infeasible interior-point algorithm for solving primal and dual geometric programs
Mathematical Programming: Series A and B - Special issue: interior point methods in theory and practice
Global Optimization of Nonconvex Polynomial Programming Problems HavingRational Exponents
Journal of Global Optimization
Analysis of Bounds for Multilinear Functions
Journal of Global Optimization
Trilinear Monomials with Mixed Sign Domains: Facets of the Convex and Concave Envelopes
Journal of Global Optimization
Journal of Global Optimization
Deterministic Global Optimization: Theory, Methods and (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 37) (Nonconvex Optimization and Its Applications)
Some transformation techniques with applications in global optimization
Journal of Global Optimization
A Superior Representation Method for Piecewise Linear Functions
INFORMS Journal on Computing
Convex underestimation strategies for signomial functions
Optimization Methods & Software - GLOBAL OPTIMIZATION
Convex relaxation for solving posynomial programs
Journal of Global Optimization
Modeling disjunctive constraints with a logarithmic number of binary variables and constraints
Mathematical Programming: Series A and B
Global solution of optimization problems with signomial parts
Discrete Optimization
Optimal design of a CMOS op-amp via geometric programming
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A reformulation framework for global optimization
Journal of Global Optimization
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Aposynomial geometric programming problem is composed of a posynomial being minimized in the objective function subject to posynomial constraints. This study proposes an efficient method to solve a posynomial geometric program with separable functions. Power transformations and exponential transformations are utilized to convexify and underestimate posynomial terms. The inverse transformation functions of decision variables generated in the convexification process are approximated by superior piecewise linear functions. The original program therefore can be converted into a convex mixed-integer nonlinear program solvable to obtain a global optimum. Several numerical experiments are presented to investigate the impact of different convexification strategies on the obtained approximate solution and to demonstrate the advantages of the proposed method in terms of both computational efficiency and solution quality.