GloptiPoly: global optimization over polynomials with Matlab and SeDuMi

By Didier Henrion, Jean B. Lasserre. Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2002

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Citations in the corpus

Pre- and Post-Processing Sum-of-Squares Programs in Practice (2009, methodology): “Compared to alternative specialized software packages for polynomial optimization based on convex optimization [10], [4], [16], the sum-of-squares module in YALMIP is entirely integrated in the general modeling framework, and can thus be used in much more advanced and general scenarios.”
Revisiting two theorems of Curto and Fialkow on moment matrices (2005, methodology): “Then, using Theorem 1.6, Lasserre [19] shows the finite convergence (in n steps); that is, p∗t = p∗ for t ≥ n.”
Optimal Designs for Rational Function Regression (2010, background): “This is an NP-hard problem even in very restricted classes of polynomials, and is known to be very diﬃcult to solve in practice even when the number of variables and the degree are rather small [20].”
PRICING A CLASS OF EXOTIC OPTIONS VIA MOMENTS AND SDP RELAXATIONS (2006, unknown): “Furthermore, these moment conditions have been applied with success in a variety of global non-convex optimisation problems (see Henrion and Lasserre (2003), and Lasserre (2001)). In the context of certain diffusions models, it is shown in Lasserre and Prieto-Rumeau (2004) that the SDP approach is i”
Complete search in continuous global optimization and constraint satisfaction (2004, methodology): “Starting quite recently, a large number of papers appeared that propose the use of semidefinite relaxations, or convex conic relaxations, to solve polynomial constraint satisfaction and global optimization problems: see, e.g., Chesi and Garulli (2001), Jibetean and De Klerk (2003), Fujie and Kojima ”
Introducing SOSTOOLS: a general purpose sum of squares programming solver (2002, background): “5A related recent software is GloptiPoly [ 4 ], which solves”
LMI Techniques for Optimization Over Polynomials in Control: A Survey (2010, methodology): “It is worth mentioning that some of these techniques are implemented in the MATLAB toolboxes GloptiPoly [36], SOSTOOLS [37] and YALMIP [38].”
Lyapunov Based Analysis and Controller Synthesis for Polynomial Systems using Sum-of-Squares Optimization (2003, methodology): “A software package to carry out this algorithm is described in [12].”
Detecting global optimality and extracting solutions in GloptiPoly (2003, methodology): “GloptiPoly is a user-friendly Matlab/SeDuMi add-on to build and solve these LMI relaxations, see [10].”
Globally optimal bilinear programming for computer vision applications (2008, background): “Note that bilinear programming is a special case of polynomial optimization, however, the problem sizes that concern us in this paper are far greater than what modern polynomial solvers can handle [12].”
Representations of positive polynomials on noncompact semialgebraic sets via KKT ideals (2007, methodology): “Using software like Gloptipoly [8] and SOSTOOLS [21], the SOS program (4.5) and (4.6) or its dual problem can be solved, and in many cases, the global minimizer x∗ and the Lagrange multiplier λ∗ can be extracted.”
Sums of Squares, Moment Matrices and Optimization Over Polynomials (2009, background): “The finite convergence result from Theorem 6.15 applies, in particular, to the case when K is contained in a discrete grid K1×. . .×Kn with Ki ⊆ R finite, considered by Lasserre [67], and by Lasserre [66] in the special case K ⊆ {0, 1}n.”
Optimality conditions and finite convergence of Lasserre’s hierarchy (2012, methodology): “However, in practical applications, hierarchy often has ﬁnite convergence, e.g., as shown by numerical experiments in Henrion and Lasserre [9, 10].”
Sums of Squares Relaxations of Polynomial Semidefinite Programs (2003, methodology): “A primal approach also produces a sequence of SDP relaxations for the polynomial SDP by extending Lasserre’s SDP relaxation method [1, 4] for POPs to the polynomial SDP.”
An analogue of the Riesz–Haviland theorem for the truncated moment problem (2008, methodology): “The Lasserre relaxations can be explicitly computed within the framework of semidefinite programming, for example, by using the software SeDuMi [24] (cf. [28, (7.5)]).”
POSITIVE POLYNOMIALS IN SCALAR AND MATRIX VARIABLES, THE SPECTRAL THEOREM AND OPTIMIZATION (2006, background): “ ideas to produce a semi-deﬁnite programming package, for a recent paper see [1]; also there is recent work of L. Vandenberghe. Semi-algebraic geometry packages are: SOS tools [PPSP04] and GloptiPoly [HL03]. A lament isthat all currentcomputational semi-algebraic geometry projects use a packaged sem”