Efficient Convexification Strategy for Generalized Geometric Programming Problems

References

• Adjiman CS, Dallwig S, Floudas CA, Neumaier A (1998) A global optimization method, αBB, for general twice differentiable constrained NLPs—I. Theoretical advances. Comput. Chemical Engrg. 22(9):1137–1158.Crossref, Google Scholar
• Akrotirianakis IG, Floudas CA (2004a) Computational experience with a new class of convex underestimators: box constrained NLP problems. J. Global Optim. 29(3):249–264.Crossref, Google Scholar
• Akrotirianakis IG, Floudas CA (2004b) A new class of improved convex underestimators for twice continuously differentiable constrained NLPs. J. Global Optim. 30(4):367–390.Crossref, Google Scholar
• Beale EML, Tomlin JA (1970) Special facilities in a general mathematical programming system for nonconvex problems using ordered sets of variables. Lawrence J, ed. Proc. 5th Internat. Conf. Oper. Res. (Tavistock Publications, London), 447–454.Google Scholar
• Björk KM, Lindberg PO, Westerlund T (2003) Some convexifications in global optimization of problems containing signomial terms. Comput. Chemical Engrg. 27(5):669–679.Crossref, Google Scholar
• Boyd SP, Kim SJ, Patil DD, Horowitz MA (2005) Digital circuit optimization via geometric programming. Oper. Res. 53(6):899–932.Link, Google Scholar
• Caratzoulas S, Floudas CA (2005) Trigonometric convex underestimator for the base functions in Fourier space. J. Optim. Theory Appl. 124(2):339–362.Crossref, Google Scholar
• Daems W, Gielen G, Sansen W (2003) Simulation-based generation of posynomial performance models for the sizing of analog integrated circuits. IEEE Trans. Comput.-Aided Design Integrated Circuits Systems 22(5):517–534.Crossref, Google Scholar
• Dam S, Mandal P (2012) Iterative performance model upgradation in geometric programming based analog circuit sizing for improved design accuracy. Proc. 25th Internat. Conf. VLSI Design (Conference Publishing Services, Los Alamitos, CA), 376–381.Google Scholar
• Floudas CA (2000) Deterministic Global Optimization: Theory, Methods and Application (Kluwer, Boston), 257–306.Crossref, Google Scholar
• Floudas CA, Akrotirianakis IG, Caratzoulas S, Meyer CA, Kallrath J (2005) Global optimization in the 21st century: advances and challenges. Comput. Chemical Engrg. 29(6):1185–1202.Crossref, Google Scholar
• Gounaris CE, Floudas CA (2008) Tight convex underestimators for C2-continuous problems: II. Multivariate functions. J. Global Optim. 42(1):69–89.Crossref, Google Scholar
• Jung H, Klein CM (2001) Optimal inventory policies under decreasing cost functions via geometric programming. Eur. J. Oper. Res. 132(3):628–642.Crossref, Google Scholar
• Kallrath J (2003) Exact computation of global minima of a nonconvex portfolio optimization problem. Floudas CA, Pardalos PM, eds. Frontiers in Global Optimization (Kluwer, Boston), 237–254.Google Scholar
• Li HL, Lu HC (2009) Global optimization for generalized geometric programs with mixed free-sign variables. Oper. Res. 57(3):701–713.Link, Google Scholar
• Li HL, Tsai JF (2005) Treating free variables in generalized geometric global optimization programs. J. Global Optim. 33(1):1–13.Crossref, Google Scholar
• Li HL, Lu HC, Huang CH, Hu NZ (2009) A superior representation method for piecewise linear functions. INFORMS J. Comput. 21(2):314–321.Link, Google Scholar
• Li W (2009) Energy efficient clustering algorithm in wireless sensor networks based on geometric programming. Proc. 2nd Internat. Sympos. Electronic Commerce Security (ISECS 09), (IEEE Computer Society, Los Alamitos, CA), 525–527.Crossref, Google Scholar
• Lindberg PO (1981) Power Convex Functions: Generalized Concavity in Optimization and Economics (Academic Publishers, Boston), 153–168.Google Scholar
• Lu HC (2012) An efficient convexification method for solving generalized geometric problems. J. Indust. Management Optim. 8(2):429–455.Crossref, Google Scholar
• Lu HC, Li HL, Gounaris CE, Floudas CA (2010) Convex relaxation for solving posynomial programs. J. Global Optim. 46(1):147–154.Crossref, Google Scholar
• Lundell A (2009) Transformation techniques for signomial functions in global optimization. PhD dissertation, Abo Akademi University, Turku, Finland.Google Scholar
• Lundell A, Westerlund T (2009a) Convex underestimation strategies for signomial functions. Optim. Methods Software. 24(4–5):505–522.Crossref, Google Scholar
• Lundell A, Westerlund T (2009b) On the relationship between power and exponential transformations for positive signomial functions. Chemical Engrg. Trans. 17:1287–1292.Google Scholar
• Lundell A, Westerlund T (2012) Global optimization of mixed-integer signomial problems in mixed integer nonlinear programming. Mixed Integer Nonlinear Programming, vol. 154 (Springer, New York), 349–369.Crossref, Google Scholar
• Lundell A, Westerlund J, Westerlund T (2009) Some transformation techniques with applications in global optimization. J. Global Optim. 43(2):391–405.Crossref, Google Scholar
• Maranas CD, Floudas CA (1997) Global optimization in generalized geometric programming. Comput. Chemical Engrg. 21(4):351–369.Crossref, Google Scholar
• Meyer CA, Floudas CA (2005) Convex envelopes for edge concave functions. Math. Programming Ser. B 103(2):207–224.Crossref, Google Scholar
• Pardalos PM, Romeijn E (2002) Global optimization: software, test problem, and applications. Handbook of Global Optimization, vol. 2 (Kluwer Academic Publishers, Boston), 515–569.Crossref, Google Scholar
• Passy U, Wilde DJ (1967) Generalized polynomial optimizations. SIAM J. Appl. Math. 15(5):1344–1356.Crossref, Google Scholar
• Pörn R, Björk KM, Westerlund T (2008) Global solution of optimization problems with signomial parts. Discrete Optim. 5(1):108–120.Crossref, Google Scholar
• Tardella F (2003) On the existence of polyhedral convex envelopes. Floudas CA, Pardalos PM, eds. Frontiers in Global Optimization (Kluwer Academic Publishers, Boston), 563–573.Google Scholar
• Tsai JF, Lin MH (2011) An efficient global approach for posynomial geometric programming problems. INFORMS J. Comput. 23(3):483–492.Link, Google Scholar
• Vielma JP, Nemhauser G (2011) Modeling disjunctive constraints with a logarithmic number of binary variables and constraints. Math. Programming 128(1):49–72.Crossref, Google Scholar