Topic
Signomial
About: Signomial is a research topic. Over the lifetime, 189 publications have been published within this topic receiving 4765 citations.
Papers published on a yearly basis
Papers
Book•
7 Dec 2010
TL;DR: The alphaBB Approach in Batch Design Under Uncertainty, the alphaBB approach in Parameter Estimation, and all Solutions of Nonlinear Constrained Systems of Equations.
Abstract: Preface. 1. Introduction. 2. Basic Concepts of Global Optimization. Part I: Biconvex and Bilinear Problems. 3. The GOP Primal-Relaxed Dual Decomposition Approach: Theory. 4. The GOP Approach: Implementation and Computational Studies. 5. The GOP Approach in Bilevel Linear and Quadratic Problems. 6. The GOP Approach in Phase and Chemical Equilibrium Problems. 7. The GOP Approach: Distributed Implementation. Part II: Signomial Problems. 8. Generalized Geometric Programming: Theory. 9. Generalized Geometric Programming: Computational Studies. Part III: Towards General Twice Differentiable NLPs. 10. From Biconvex to General Twice Differentiable NLPs. 11. The alphaBB For Box Constrained Twice-Differentiable NLPs: Theory. 12. The alphaBB for Constrained Twice-Differentiable NLPs: Theory. 13. Computational Studies of the alphaBB Approach. 14. Global Optimization in Microclusters. 15. The alphaBB Approach in Molecular Structure Prediction. 16. The alphaBB Approach in Protein Folding. 17. The alphaBB Approach in Peptide Docking. 18. The alphaBB Approach in Batch Design Under Uncertainty. 19. The alphaBB Approach in Parameter Estimation. Part IV: Nonlinear and Mixed-Integer Optimization. 20. Introduction to Nonlinear and Mixed-Integer Optimization. 21. The SMIN-alphaBB Approach: Theory and Computations. 22. The GMIN-alphaBB Approach: Theory and Computations. Part V: Nonlinear Constrained Systems of Equations. 23. All Solutions of Nonlinear Constrained Systems of Equations. 24. Locating all Homogeneous Azeotropes. References. Index.
578 citations
TL;DR: The purpose of this paper is to show how the extensible structure of ANTIGONE realizes the authors' previously-proposed mixed- integer quadratically-constrained quadratic program and mixed-integer signomial optimization computational frameworks.
Abstract: This manuscript introduces ANTIGONE, Algorithms for coNTinuous/Integer Global Optimization of Nonlinear Equations, a general mixed-integer nonlinear global optimization framework. ANTIGONE is the evolution of the Global Mixed-Integer Quadratic Optimizer, GloMIQO, to general nonconvex terms. The purpose of this paper is to show how the extensible structure of ANTIGONE realizes our previously-proposed mixed-integer quadratically-constrained quadratic program and mixed-integer signomial optimization computational frameworks. To demonstrate the capacity of ANTIGONE, this paper presents computational results on a test suite of $$2{,}571$$ 2 , 571 problems from standard libraries and the open literature; we compare ANTIGONE to other state-of-the-art global optimization solvers.
537 citations
TL;DR: In this paper, the difference of two polynomials with arbitrary real exponents, but positive coefficients and positive independent variables, is termed asignomial, and the resulting class of posynomial programs is substantially larger than the class of prototype geometric programs.
Abstract: The difference of twoposynomials (namely, polynomials with arbitrary real exponents, but positive coefficients and positive independent variables) is termed asignomial. Each signomial program (in which a signomial is to be either minimized or maximized subject to signomial constraints) is transformed into an equivalent posynomial program in which a posynomial is to be minimized subject only to inequality posynomial constraints. The resulting class of posynomial programs is substantially larger than the class of (prototype)geometric programs (namely, posynomial programs in which a posynomial is to be minimized subject only to upper-bound inequality posynomial constraints). However, much of the (prototype) geometric programming theory is generalized by studying theequilibrium solutions to thereversed geometric programs in this larger class. Actually, some of this theory is new even when specialized to the class of prototype geometric programs. On the other hand, all of it can indirectly, but easily, be applied to the much larger class of well-posedalgebraic programs (namely, programs involving real-valued functions that are generated solely by addition, subtraction, multiplication, division, and the extraction of roots).
148 citations
TL;DR: In this paper, a hierarchy of convex relaxations is proposed to obtain successively tighter lower bounds of the optimal value of SPs, which are obtained by solving increasingly larger-sized relative entropy optimization problems and are convex programs specified in terms of linear and relative entropy functions.
Abstract: Signomial programs (SPs) are optimization problems specified in terms of signomials, which are weighted sums of exponentials composed with linear functionals of a decision variable. SPs are nonconvex optimization problems in general, and families of NP-hard problems can be reduced to SPs. In this paper we describe a hierarchy of convex relaxations to obtain successively tighter lower bounds of the optimal value of SPs. This sequence of lower bounds is computed by solving increasingly larger-sized relative entropy optimization problems, which are convex programs specified in terms of linear and relative entropy functions. Our approach relies crucially on the observation that the relative entropy function, by virtue of its joint convexity with respect to both arguments, provides a convex parametrization of certain sets of globally nonnegative signomials with efficiently computable nonnegativity certificates via the arithmetic-geometric-mean inequality. By appealing to representation theorems from real algeb...
121 citations
TL;DR: The tractability and effectiveness of the proposed successive convexification framework is demonstrated, and some considerations are presented to investigate the convergence properties of the algorithm and to give a performance comparison between the proposed approach and the current methods.
102 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 11 |
| 2020 | 9 |
| 2019 | 14 |
| 2018 | 10 |
| 2017 | 12 |
| 2016 | 8 |