
INTLAB
 Referenced in 435 articles
[sw04004]
 structured matrices) sparse s.p.d. linear systems systems of nonlinear equations (including unconstrained optimization) roots ... clusters) quadrature for univariate functions univariate polynomial zeros (simple and clusters) interval arithmetic for real ... fast) interval arithmetic for real and complex sparse matrices (very fast) automatic differentiation (forward mode ... systems of nonlinear equations) Hessians (for global optimization) Taylor series for univariate functions automatic slopes...

SparsePOP
 Referenced in 65 articles
[sw04331]
 SparsePOP: a sparse semidefinite programming relaxation of polynomial optimization problems. SparsePOP is a Matlab implementation ... polynomial optimization problem (POP) proposed by Waki et al. [2006]. The sparse SDP relaxation exploits ... sparse structure of polynomials in POPs when applying “a hierarchy of LMI relaxations of increasing ... efficiency of SparsePOP to approximate optimal solutions of POPs is thus increased, and largerscale...

SparseBSOS
 Referenced in 12 articles
[sw31772]
 large scale polynomial optimization with sparsity. We provide a sparse version of the bounded degree ... Comp Optim:87–117, 2017) for polynomial optimization problems. It permits to treat large scale ... pattern satisfies the running intersection property this SparseBSOS hierarchy of semidefinite programs (with semidefinite...

Aztec
 Referenced in 83 articles
[sw12817]
 GaussSeidel, leastsquares polynomials, and overlapping domain decomposition using sparse LU, ILU, ILUT, BILU ... supports two different sparse matrix notations: a) a pointentry modified sparse row (MSR) format ... parallel implementation and the library includes highly optimized matrixvector multiply kernels and preconditioners...

Tensorlab
 Referenced in 53 articles
[sw14255]
 with structured factors and support for dense, sparse and incomplete data sets, tensor decompositions: canonical ... approximation (LMLRA), complex optimization: quasiNewton and nonlinearleast squares optimization with complex variables including ... numerical complex differentiation, global minimization of bivariate polynomials and rational functions: both real and complex...

Ncpol2sdpa
 Referenced in 3 articles
[sw17564]
 Algorithm 950: Ncpol2sdpa  sparse semidefinite programming relaxations for polynomial optimization problems of noncommuting variables...

NSWC
 Referenced in 11 articles
[sw09119]
 functions, polynomials, vectors, matrices, large dense systems of linear equations, banded matrices, sparse matrices, eigenvalues ... equations, leastsquares solution of linear equations, optimization, transforms, approximation of functions, curve fitting, surface...

BBCPOP
 Referenced in 3 articles
[sw31757]
 hierarchy of sparse doubly nonnegative (DNN) relaxations of a class of polynomial optimization (minimization) problems...

PSOPT
 Referenced in 8 articles
[sw20700]
 solve optimal control problems by approximating the timedependent variables using global polynomials, such ... nodes. Sparse nonlinear programming is then used to find local optimal solutions. PSOPT is able...

StdPoolingPolyAlgos
 Referenced in 5 articles
[sw34823]
 structure in the pooling problem: from sparse stronglypolynomial solutions to NPhardness. The standard ... hard subclass of nonconvex quadraticallyconstrained optimization problems that commonly arises in process systems ... pooling problem sparsity and show that the sparse patterns of active topological structure are associated...

SingularIntegralEquations
 Referenced in 8 articles
[sw22771]
 intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the equations as almostbanded infinite ... accomplished by utilizing low rank approximations for sparse representations of the bivariate kernels. The resulting ... bandwidth and n is the optimal number of unknowns needed to resolve the true solution...

CGPOPS
 Referenced in 1 article
[sw35933]
 transcribe the continuous optimal control problem into a large sparse nonlinear programming problem ... intervals and the degree of the approximating polynomial within each mesh interval to achieve ... software is demonstrated on five optimal control problems of varying complexity. The software described...

RLTPOS
 Referenced in 3 articles
[sw18321]
 linearization techniquebased opensource optimization software for solving polynomial programming problems ... representations, and (2) semidefinite cuts for sparse problems. We present computational results using instances from...

NLCertify
 Referenced in 4 articles
[sw08786]
 transcendental multivariate functions. The tool exploits sparse semialgebraic optimization techniques with approximation methods for transcendental ... semialgebraic functions obtained by composition of polynomials with some basic operations (including the square root...

borderbasix
 Referenced in 1 article
[sw16958]
 from multiplication matrices, real radical computation, polynomial optimization. The implementation parameterized by the coefficient type ... provides a versatile family of tools for polynomial computation with modular arithmetic, floating point arithmetic ... linear algebra solvers for dense and sparse matrices for these various types of coefficients...

ACRITHXSC
 Referenced in 49 articles
[sw00015]
 ACRITHXSC is a Fortranlike programming language...

ADOLC
 Referenced in 242 articles
[sw00019]
 ADOLC: Automatic Differentiation of C/C++. We present...

AMD
 Referenced in 55 articles
[sw00039]
 Algorithm 837: AMD is a set of routines...

ANSYS
 Referenced in 663 articles
[sw00044]
 ANSYS offers a comprehensive software suite that spans...

ATLAS
 Referenced in 197 articles
[sw00056]
 This paper describes the Automatically Tuned Linear Algebra...