- Referenced in 301 articles
- important applications in various fields such as optimization, probability, finance, control, signal processing, chemistry, cristallography ... moment problems with polynomial data. Many important applications in e.g. optimization, probability, financial economics ... optimal control, can be viewed as particular instances of the GPM, and (possibly after some ... transformation) of the GPM with polynomial data.The approach is similar to that used...
- Referenced in 65 articles
- sparse semidefinite programming relaxation of polynomial optimization problems. SparsePOP is a Matlab implementation ... global optimal solution of a polynomial optimization problem (POP) proposed by Waki ... relaxation exploits a sparse structure of polynomials in POPs when applying “a hierarchy ... efficiency of SparsePOP to approximate optimal solutions of POPs is thus increased, and larger-scale...
- Referenced in 426 articles
- systems systems of nonlinear equations (including unconstrained optimization) roots of univariate and multivariate nonlinear equations ... clusters) quadrature for univariate functions univariate polynomial zeros (simple and clusters) interval arithmetic for real ... systems of nonlinear equations) Hessians (for global optimization) Taylor series for univariate functions automatic slopes ... simple) univariate functions univariate and multivariate (interval) polynomials rigorous real interval standard functions (fast, very...
- Referenced in 740 articles
- syntax; analytic differentiation and integration; factorization of polynomials; facilities for the solution of a variety ... variety of formats; facilities for generating optimized numerical programs from symbolic input; calculations with...
- Referenced in 213 articles
- isolating the real roots of a univariate polynomial using Descartes’ rule of signs. It follows ... algorithm is presented, which is optimal in terms of memory usage and as fast ... Krandick’s variant, independently of the input polynomial. From this new algorithm, we derive ... critical optimizations have important consequences since our new algorithm still works with huge polynomials, including...
- Referenced in 273 articles
- optimization programs. SOSTOOLS can be used to specify and solve sum of squares polynomial problems...
- Referenced in 36 articles
- SMRSOFT: a MATLAB toolbox for optimization over polynomials and dynamical systems study via SOS programming ... Matlab toolbox for solving basic optimization problems over polynomials and studying dynamical systems...
- Referenced in 18 articles
- terms that arise in nonconvex mixed integer optimization problems. The goal is to obtain ... produce a solver for mixed integer polynomial optimization problems...
- Referenced in 12 articles
- SOSOPT: A Toolbox for Polynomial Optimization. SOSOPT is a Matlab toolbox for formulating and solving ... Squares (SOS) polynomial optimizations. This document briefly describes the use and functionality of this toolbox...
- Referenced in 11 articles
- degree SOS hierarchy for large scale polynomial optimization with sparsity. We provide a sparse version ... Comp Optim:87–117, 2017) for polynomial optimization problems. It permits to treat large scale...
- Referenced in 32 articles
- algorithm which can attain near-optimal average reward in polynomial time ... environment and acts based on the optimal policy derived from this model. The model...
- Referenced in 53 articles
- squares optimization with complex variables including numerical complex differentiation, global minimization of bivariate polynomials ... real exact plane search (PS) for tensor optimization, and much more: cumulants, tensor visualization, estimating...
- Referenced in 5 articles
- sparsity. This paper is concerned with polynomial optimization problems. We show how to exploit term ... applied to compute lower bounds for polynomial optimization problems either randomly generated or coming from...
- Referenced in 49 articles
- optimization solvers, a integrated set of routines for function approximation using polynomial, splines and other...
- Referenced in 13 articles
- LinearPseudo-Boolean Optimization , 0-1 variables, objective and constraints polynomial(C++) A Davis-Putnam Based...
- Referenced in 5 articles
- SPOT (Systems Polynomial Optimization Tools) is a MATLAB toolbox written as an alternative implementation ... R2009a). SPOT provides its own matrix multivariable polynomial variable class msspoly ... handling elementary polynomial operations, a special class mssprog for defining convex optimization problems...
- Referenced in 8 articles
- multistep and multistage methods. polyopt: Find optimal stability polynomials of a given degree and order...
- Referenced in 3 articles
- Ncpol2sdpa -- sparse semidefinite programming relaxations for polynomial optimization problems of noncommuting variables. A hierarchy ... relaxations approximates the global optimum of polynomial optimization problems of noncommuting variables. Generating the relaxation...
- Referenced in 15 articles
- designed to work specifically with optimization problems presenting parameter-dependent variables with parameters ... simplex. The variables are assumed to depend polynomially ... parameters, being the polynomials considered to be homogeneous. Such optimization problems arise, for example...
- Referenced in 4 articles
- infeasibility. It does not rely on any optimization solver: the only subroutine it needs ... literature, with many SDPs coming from polynomial optimization...