Convergent SDP‐Relaxations in Polynomial Optimization with Sparsity

From MaRDI portal
Publication:5757351

DOI10.1137/05064504XzbMath1119.90036OpenAlexW2071550336MaRDI QIDQ5757351

Jean-Bernard Lasserre

Publication date: 6 September 2007

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/05064504x



Related Items

Minimizing the sum of many rational functions, Amoebas, nonnegative polynomials and sums of squares supported on circuits, LP relaxations for a class of linear semi-infinite programming problems, Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational Coefficients, Dual Certificates and Efficient Rational Sum-of-Squares Decompositions for Polynomial Optimization over Compact Sets, Semidefinite programming relaxation methods for global optimization problems with sparse polynomials and unbounded semialgebraic feasible sets, A convex relaxation approach to set-membership identification of LPV systems, Semidefinite Approximations of Projections and Polynomial Images of SemiAlgebraic Sets, Moments and sums of squares for polynomial optimization and related problems, Approximate gcds of polynomials and sparse SOS relaxations, Sparse noncommutative polynomial optimization, Set-membership errors-in-variables identification of MIMO linear systems, Mining for diamonds -- matrix generation algorithms for binary quadratically constrained quadratic problems, Continuous multifacility ordered median location problems, Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO, Sparse-BSOS: a bounded degree SOS hierarchy for large scale polynomial optimization with sparsity, Duality of sum of nonnegative circuit polynomials and optimal SONC bounds, RLT-POS: reformulation-linearization technique-based optimization software for solving polynomial programming problems, Certifying the global optimality of quartic minimization over the sphere, Correlative sparsity structures and semidefinite relaxations for concave cost transportation problems with change of variables, Canonical primal-dual algorithm for solving fourth-order polynomial minimization problems, Solving polynomial least squares problems via semidefinite programming relaxations, Symmetry Reduction in AM/GM-Based Optimization, Bounded error identification of Hammerstein systems through sparse polynomial optimization, Cutting Plane Generation through Sparse Principal Component Analysis, Welfare-maximizing correlated equilibria using Kantorovich polynomials with sparsity, Optimization on the Euclidean Unit Sphere, Exploiting sparsity for the min \(k\)-partition problem, Partitioning procedure for polynomial optimization, Theoretical filtering of RLT bound-factor constraints for solving polynomial programming problems to global optimality, Partial Lasserre relaxation for sparse Max-Cut, One-shot set-membership identification of generalized Hammerstein-Wiener systems, A hierarchy of spectral relaxations for polynomial optimization, Semidefinite Relaxation Methods for Tensor Absolute Value Equations, A unified framework for the identification of a general class of multivariable nonlinear block‐structured systems, An algorithm for semi-infinite polynomial optimization, Discussion on: ``A decomposition algorithm for KYP-SDPs, A new scheme for approximating the weakly efficient solution set of vector rational optimization problems, Exploiting ideal-sparsity in the generalized moment problem with application to matrix factorization ranks, A Correlatively Sparse Lagrange Multiplier Expression Relaxation for Polynomial Optimization, Modal occupation measures and LMI relaxations for nonlinear switched systems control, Construction of Multivariate Polynomial Approximation Kernels via Semidefinite Programming, Conic linear optimization for computer-assisted proofs. Abstracts from the workshop held April 10--16, 2022, A Multigrid Approach to SDP Relaxations of Sparse Polynomial Optimization Problems, Sum-of-squares chordal decomposition of polynomial matrix inequalities, Optimizing \(n\)-variate \((n+k)\)-nomials for small \(k\), Enclosing ellipsoids and elliptic cylinders of semialgebraic sets and their application to error bounds in polynomial optimization, Exploiting sparsity for semi-algebraic set volume computation, Min-max and robust polynomial optimization, Bounds on mean energy in the Kuramoto–Sivashinsky equation computed using semidefinite programming, Semidefinite programming for min-max problems and games, The \(\mathcal A\)-truncated \(K\)-moment problem, Exploiting term sparsity in noncommutative polynomial optimization, A multilevel analysis of the Lasserre hierarchy, Stable rank-one matrix completion is solved by the level \(2\) Lasserre relaxation, TSSOS: A Moment-SOS Hierarchy That Exploits Term Sparsity, Chordal-TSSOS: A Moment-SOS Hierarchy That Exploits Term Sparsity with Chordal Extension, LP Formulations for Polynomial Optimization Problems, Minimizing Rational Functions: A Hierarchy of Approximations via Pushforward Measures, Improved parameter bounds for set-membership EIV problems, SDP RELAXATIONS FOR QUADRATIC OPTIMIZATION PROBLEMS DERIVED FROM POLYNOMIAL OPTIMIZATION PROBLEMS, Compatibility, desirability, and the running intersection property, Monomial-wise optimal separable underestimators for mixed-integer polynomial optimization, Exact Certification in Global Polynomial Optimization Via Rationalizing Sums-Of-Squares, A polynomial optimization approach to constant rebalanced portfolio selection, Bounding the parameters of block‐structured nonlinear feedback systems, Optimizing ordered median functions with applications to single facility location, Penalized semidefinite programming for quadratically-constrained quadratic optimization, Exploiting sparsity in linear and nonlinear matrix inequalities via positive semidefinite matrix completion, Decomposition-based method for sparse semidefinite relaxations of polynomial optimization problems, Approximating Pareto curves using semidefinite relaxations, A semidefinite programming approach to the generalized problem of moments, Robustness to Dependency in Portfolio Optimization Using Overlapping Marginals, Positive polynomials on projective limits of real algebraic varieties, A note on sparse SOS and SDP relaxations for polynomial optimization problems over symmetric cones, Introduction to Semidefinite, Conic and Polynomial Optimization, Positivity and Optimization: Beyond Polynomials, Exploiting Sparsity in SDP Relaxation of Polynomial Optimization Problems, Algorithm 996, Perturbed sums-of-squares theorem for polynomial optimization and its applications, A prolongation-projection algorithm for computing the finite real variety of an ideal, A sublevel moment-SOS hierarchy for polynomial optimization, Finding unstable periodic orbits: a hybrid approach with polynomial optimization, Unconstrained minimization of block-circulant polynomials via semidefinite program in third-order tensor space, AC optimal power flow: a conic programming relaxation and an iterative MILP scheme for global optimization, A convex optimization approach to synthesizing state feedback data-driven controllers for switched linear systems, New limits of treewidth-based tractability in optimization