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A survey of hidden convex optimization (Q2176821)

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Language	Label	Description	Also known as
English	A survey of hidden convex optimization	scientific article

Statements

scholarly article

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A survey of hidden convex optimization (English)

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Journal of the Operations Research Society of China

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publication date

5 May 2020

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full work available at URL

https://arxiv.org/abs/1902.10921

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zbMATH Keywords

convex programming

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quadratic programming

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quadratic matrix programming

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fractional programming

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Lagrangian dual

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semidefinite programming

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MaRDI profile type

MaRDI publication profile

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NP-hardness of deciding convexity of quartic polynomials and related problems

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Matrix <i>p</i>-Norms Are NP-Hard to Approximate If $p\neq1,2,\infty$

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On the copositive representation of binary and continuous nonconvex quadratic programs

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Some NP-complete problems in quadratic and nonlinear programming

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Hidden convexity in some nonconvex quadratically constrained quadratic programming

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On the convexification of nonlinear programming problems: An applications-oriented survey

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Hidden convex minimization

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Peeling Off a Nonconvex Cover of an Actual Convex Problem: Hidden Convexity

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On The Reduction of Duality Gap in Box Constrained Nonconvex Quadratic Program

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Zero duality gap for a class of nonconvex optimization problems

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Towards strong duality in integer programming

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Local saddle point and a class of convexification methods for nonconvex optimization problems

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Convexification, concavification and monotonization in global optimization

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Strong duality in optimization: shifted power reformulation

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Computation of Minimum-Volume Covering Ellipsoids

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\(NP\)-hardness of linear multiplicative programming and related problems

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Programming with linear fractional functionals

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Parameter-free convex equivalent and dual programs of fractional programming problems

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A sequential method for a class of pseudoconcave fractional problems

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Minimizing the sum of a linear and a linear fractional function applying conic quadratic representation: continuous and discrete problems

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Computing Optimal Locally Constrained Steps

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Recent advances in trust region algorithms

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Quadratically constrained least squares and quadratic problems

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Local Minimizers of Quadratic Functions on Euclidean Balls and Spheres

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Indefinite Trust Region Subproblems and Nonsymmetric Eigenvalue Perturbations

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Theory and application of <i>p</i>-regularized subproblems for <i>p</i>>2

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A survey for the quadratic assignment problem

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Applications of parametric programming and eigenvalue maximization to the quadratic assignment problem

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Strong duality for a trust-region type relaxation of the quadratic assignment problem

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Global optimization of a class of nonconvex quadratically constrained quadratic programming problems

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Feasibility testing for systems of real quadratic equations

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The generalized trust region subproblem

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On the Solution of the GPS Localization and Circle Fitting Problems

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Strong duality for generalized trust region subproblem: S-lemma with interval bounds

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A Survey of the S-Lemma

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S-lemma with equality and its applications

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Hidden conic quadratic representation of some nonconvex quadratic optimization problems

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SOCP reformulation for the generalized trust region subproblem via a canonical form of two symmetric matrices

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Convexity of quadratic transformations and its use in control and optimization

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Parametric Lagrangian dual for the binary quadratic programming problem

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Strong Duality in Nonconvex Quadratic Optimization with Two Quadratic Constraints

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Semidefinite programming relaxations for the quadratic assignment problem

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A note on lack of strong duality for quadratic problems with orthogonal constraints

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On Lagrangian Relaxation of Quadratic Matrix Constraints

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On Equivalence of Semidefinite Relaxations for Quadratic Matrix Programming

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Nondifferentiable optimization and polynomial problems

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Maxima for Graphs and a New Proof of a Theorem of Turán

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Tightening a copositive relaxation for standard quadratic optimization problems

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Computable representations for convex hulls of low-dimensional quadratic forms

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Fractional Programming. I, Duality

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A convex optimization approach for minimizing the ratio of indefinite quadratic functions over an ellipsoid

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An SDP approach for quadratic fractional problems with a two-sided quadratic constraint

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On Lagrangian duality gap of quadratic fractional programming with a two-sided quadratic constraint

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Finding a Global Optimal Solution for a Quadratically Constrained Fractional Quadratic Problem with Applications to the Regularized Total Least Squares

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Quadratic Matrix Programming

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On the Solution of the Tikhonov Regularization of the Total Least Squares Problem

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Efficiently solving total least squares with Tikhonov identical regularization

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Duallity and sensitivity in nonconvex quadratic optimization over an ellipsoid

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A linear-time algorithm for the trust region subproblem based on hidden convexity

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A Second-Order Cone Based Approach for Solving the Trust-Region Subproblem and Its Variants

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A linear-time algorithm for trust region problems

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Successive Lagrangian relaxation algorithm for nonconvex quadratic optimization

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Convex Relaxations of the Weighted Maxmin Dispersion Problem

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On the Ball-Constrained Weighted Maximin Dispersion Problem

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A semidefinite framework for trust region subproblems with applications to large scale minimization

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On the Rank of Extreme Matrices in Semidefinite Programs and the Multiplicity of Optimal Eigenvalues

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On Cones of Nonnegative Quadratic Functions

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New Results on Quadratic Minimization

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Quadratic optimization over a second-order cone with linear equality constraints

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Second-Order-Cone Constraints for Extended Trust-Region Subproblems

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The trust region subproblem with non-intersecting linear constraints

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How to convexify the intersection of a second order cone and a nonconvex quadratic

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Recovering optimal solutions via SOC-SDP relaxation of trust region subproblem with nonintersecting linear constraints

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A new semidefinite programming relaxation scheme for a class of quadratic matrix problems

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Quadratic programs with hollows

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A Note on Polynomial Solvability of the CDT Problem

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On the complexity of quadratic programming with two quadratic constraints

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Solving Generalized CDT Problems via Two-Parameter Eigenvalues

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Polynomial Solvability of Variants of the Trust-Region Subproblem

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A generalized solution of the orthogonal Procrustes problem

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On minimizing a quadratic function on Stiefel manifold

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On a self-consistent-field-like iteration for maximizing the sum of the Rayleigh quotients

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A Linear-Time Algorithm for Globally Maximizing the Sum of a Generalized Rayleigh Quotient and a Quadratic Form on the Unit Sphere

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Potpourri of Conjectures and Open Questions in Nonlinear Analysis and Optimization

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The Legendre–Fenchel Conjugate of the Product of Two Positive Definite Quadratic Forms

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A note on Legendre-Fenchel conjugate of the product of two positive-definite quadratic forms

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On local convexity of quadratic transformations

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On the convexity of a class of quadratic mappings and its application to the problem of finding the smallest ball enclosing a given intersection of balls

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Convexity properties associated with nonconvex quadratic matrix functions and applications to quadratic programming

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Identifiers

zbMATH Open document ID

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10.1007/s40305-019-00286-5

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2176821

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