Signomial and polynomial optimization via relative entropy and partial dualization

[1]  A. K. Rigler,et al.  A penalty treatment of equality constraints in generalized geometric programming , 1982 .

[2]  Yuan Ma,et al.  A robust algorithm for generalized geometric programming , 2008, J. Glob. Optim..

[3]  H. Koeppl,et al.  Global injectivity and multiple equilibria in uni- and bi-molecular reaction networks , 2012 .

[4]  Peiping Shen,et al.  Global optimization of signomial geometric programming using linear relaxation , 2004, Appl. Math. Comput..

[5]  J. Maurice Rojas,et al.  Optimization and NP_R-completeness of certain fewnomials , 2009, SNC '09.

[6]  Martin A. York,et al.  Application of Signomial Programming to Aircraft Design , 2017 .

[7]  Adrian S. Lewis,et al.  Convex Analysis And Nonlinear Optimization , 2000 .

[8]  Katta G. Murty,et al.  Some NP-complete problems in quadratic and nonlinear programming , 1987, Math. Program..

[9]  M. Powell A Direct Search Optimization Method That Models the Objective and Constraint Functions by Linear Interpolation , 1994 .

[10]  Thorsten Theobald,et al.  A unified framework of SAGE and SONC polynomials and its duality theory , 2019, Math. Comput..

[11]  Allen Silver,et al.  Beta , 1975, The SAGE Encyclopedia of Research Design.

[12]  Shashwati Ray,et al.  An efficient algorithm for range computation of polynomials using the Bernstein form , 2009, J. Glob. Optim..

[13]  Shanhe Wu,et al.  Some Retarded Difference Inequalities of Product Form and Their Application , 2014 .

[14]  Heinz Koeppl,et al.  Finding invariant sets for biological systems using monomial domination , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[15]  V. Chandrasekaran,et al.  Newton Polytopes and Relative Entropy Optimization , 2018, Foundations of Computational Mathematics.

[16]  J. Lasserre An Introduction to Polynomial and Semi-Algebraic Optimization , 2015 .

[17]  Gongxian Xu,et al.  Global optimization of signomial geometric programming problems , 2014, Eur. J. Oper. Res..

[18]  N. Z. Shor Class of global minimum bounds of polynomial functions , 1987 .

[19]  James Yan Signomial programs with equality constraints : numerical solution and applications , 1976 .

[20]  Stephen P. Boyd,et al.  ECOS: An SOCP solver for embedded systems , 2013, 2013 European Control Conference (ECC).

[21]  Parikshit Shah,et al.  Relative Entropy Relaxations for Signomial Optimization , 2014, SIAM J. Optim..

[22]  G. Bard Some Basic Facts about Linear Algebra over \(\mathbb{G}\mathbb{F}\)(2) , 2009 .

[23]  Stephen P. Boyd,et al.  Disciplined geometric programming , 2018, Optimization Letters.

[24]  Jean B. Lasserre,et al.  Sparse-BSOS: a bounded degree SOS hierarchy for large scale polynomial optimization with sparsity , 2016, Mathematical Programming Computation.

[25]  B. Reznick,et al.  Polynomials that are positive on an interval , 2000 .

[26]  Didier Henrion,et al.  GloptiPoly 3: moments, optimization and semidefinite programming , 2007, Optim. Methods Softw..

[27]  Amir Ali Ahmadi,et al.  DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization , 2017, SIAM J. Appl. Algebra Geom..

[28]  B. Reznick Forms derived from the arithmetic-geometric inequality , 1989 .

[29]  Jean B. Lasserre,et al.  Global Optimization with Polynomials and the Problem of Moments , 2000, SIAM J. Optim..

[30]  S. Mizutani On MINDEP of the University of British Columbia , 1976 .

[31]  Brian S. Cohen,et al.  Comparison of Algorithms for Including Equality Constraints in Signomial Programming ACDL Technical Report TR-2017-1 , 2017 .

[32]  P. Parrilo Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization , 2000 .

[33]  Rabih A. Jabr Inductor design using signomial programming , 2007 .

[34]  Yanjun Wang,et al.  A deterministic global optimization algorithm for generalized geometric programming , 2005, Appl. Math. Comput..

[35]  Timo de Wolff,et al.  The Algebraic Boundary of the Sonc-Cone , 2019, SIAM J. Appl. Algebra Geom..

[36]  M. Laurent Sums of Squares, Moment Matrices and Optimization Over Polynomials , 2009 .

[37]  Timo de Wolff,et al.  Amoebas, nonnegative polynomials and sums of squares supported on circuits , 2014, 1402.0462.

[38]  Peiping Shen,et al.  A Global Optimization Algorithm for Signomial Geometric Programming Problem , 2014 .

[39]  Shao-Jian Qu,et al.  A new global optimization algorithm for signomial geometric programming via Lagrangian relaxation , 2007, Appl. Math. Comput..

[40]  Mung Chiang,et al.  Nonconvex Optimization for Communication Networks , 2009 .

[41]  Jean B. Lasserre,et al.  A bounded degree SOS hierarchy for polynomial optimization , 2015, EURO J. Comput. Optim..

[42]  Peiping Shen,et al.  A new rectangle branch-and-pruning approach for generalized geometric programming , 2006, Appl. Math. Comput..

[43]  Pablo A. Parrilo,et al.  SOSTOOLS Version 3.00 Sum of Squares Optimization Toolbox for MATLAB , 2013, ArXiv.

[44]  Edward Burnell,et al.  GPkit: A Human-Centered Approach to Convex Optimization in Engineering Design , 2020, CHI.

[45]  Jan Verschelde,et al.  Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation , 1999, TOMS.

[46]  Timo de Wolff,et al.  An Experimental Comparison of SONC and SOS Certificates for Unconstrained Optimization , 2018, ArXiv.