SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2009, Volume 31, Issue 3, pp. 1235 - 1256

The nuclear norm (sum of singular values) of a matrix is often used in convex heuristics for rank minimization problems in control, signal processing, and...

Nuclear norm approximation | Semidefinite programming | Interior-point methods | System identification | Subspace algorithm | Matrix rank minimization | MATHEMATICS, APPLIED | interior-point methods | matrix rank minimization | SEMIDEFINITE | semidefinite programming | SHAPE | MOTION | MINIMIZATION | subspace algorithm | nuclear norm approximation | OPTIMIZATION | system identification | TOTAL LEAST-SQUARES

Nuclear norm approximation | Semidefinite programming | Interior-point methods | System identification | Subspace algorithm | Matrix rank minimization | MATHEMATICS, APPLIED | interior-point methods | matrix rank minimization | SEMIDEFINITE | semidefinite programming | SHAPE | MOTION | MINIMIZATION | subspace algorithm | nuclear norm approximation | OPTIMIZATION | system identification | TOTAL LEAST-SQUARES

Journal Article

Journal of Machine Learning Research, ISSN 1532-4435, 10/2010, Volume 11, pp. 2671 - 2705

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 10/2019, Volume 183, Issue 1, pp. 179 - 198

The Douglasâ€“Rachford method is a popular splitting technique for finding a zero of the sum of two subdifferential operators of proper, closed, and convex...

Lipschitz continuous mapping | Secondary 49M29 | Mathematics | Theory of Computation | Strongly monotone operator | Optimization | Strongly convex function | Skew-symmetric operator | Linear convergence | Primary 47H05 | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | Douglasâ€“Rachford algorithm | 47H09 | 49M27 | 49N15 | Applications of Mathematics | Engineering, general | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford algorithm | INCLUSIONS | ALGORITHMS | Electrical engineering | Algorithms | Operators (mathematics) | Splitting | Convergence

Lipschitz continuous mapping | Secondary 49M29 | Mathematics | Theory of Computation | Strongly monotone operator | Optimization | Strongly convex function | Skew-symmetric operator | Linear convergence | Primary 47H05 | Calculus of Variations and Optimal Control; Optimization | 90C25 | Operations Research/Decision Theory | Douglasâ€“Rachford algorithm | 47H09 | 49M27 | 49N15 | Applications of Mathematics | Engineering, general | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford algorithm | INCLUSIONS | ALGORITHMS | Electrical engineering | Algorithms | Operators (mathematics) | Splitting | Convergence

Journal Article

IEEE Transactions on Power Systems, ISSN 0885-8950, 07/2014, Volume 29, Issue 4, pp. 1855 - 1863

We propose a new method for generating semidefinite relaxations of optimal power flow problems. The method is based on chordal conversion techniques: by...

Chordal conversion | Transmission line matrix methods | Power transmission lines | optimal power flow | Generators | System-on-chip | Linear matrix inequalities | semi definite relaxation | Equations | Optimization | semidefinite relaxation | SPARSITY | OPTIMIZATION | INTERIOR-POINT METHODS | SDP | ENGINEERING, ELECTRICAL & ELECTRONIC | Finite element method | Usage | Numerical analysis | Electric power systems | Mathematical optimization | Innovations | Computation | Power flow | Mathematical models | Computational efficiency | Conversion | Standards | Teknik och teknologier | Engineering and Technology | Elektroteknik och elektronik | Chordal conversion; optimal power flow; semidefinite relaxation | Electrical Engineering, Electronic Engineering, Information Engineering

Chordal conversion | Transmission line matrix methods | Power transmission lines | optimal power flow | Generators | System-on-chip | Linear matrix inequalities | semi definite relaxation | Equations | Optimization | semidefinite relaxation | SPARSITY | OPTIMIZATION | INTERIOR-POINT METHODS | SDP | ENGINEERING, ELECTRICAL & ELECTRONIC | Finite element method | Usage | Numerical analysis | Electric power systems | Mathematical optimization | Innovations | Computation | Power flow | Mathematical models | Computational efficiency | Conversion | Standards | Teknik och teknologier | Engineering and Technology | Elektroteknik och elektronik | Chordal conversion; optimal power flow; semidefinite relaxation | Electrical Engineering, Electronic Engineering, Information Engineering

Journal Article

Optimization and Engineering, ISSN 1389-4420, 3/2007, Volume 8, Issue 1, pp. 67 - 127

A geometric program (GP) is a type of mathematical optimization problem characterized by objective and constraint functions that have a special form. Recently...

Systems Theory, Control | Convex optimization | Operations Research/Decision Theory | Mathematics | Agriculture | Engineering, general | Interior-point methods | GeneralizedÂ geometricÂ programming | Optimization | Environmental Management | Geometric programming | Generalized geometric programming | VARYING ORDER COST | MAXIMUM-LIKELIHOOD | interior-point methods | OPTIMAL-DESIGN | SIMULTANEOUS GATE | geometric programming | 2 RESTRICTIONS | SIMULTANEOUS BUFFER | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | generalized geometric programming | GLOBAL OPTIMIZATION | convex optimization | ELMORE DELAY | INVENTORY MODEL | SENSITIVITY ANALYSIS | Physicians (General practice) | Studies | Problems | Operations research

Systems Theory, Control | Convex optimization | Operations Research/Decision Theory | Mathematics | Agriculture | Engineering, general | Interior-point methods | GeneralizedÂ geometricÂ programming | Optimization | Environmental Management | Geometric programming | Generalized geometric programming | VARYING ORDER COST | MAXIMUM-LIKELIHOOD | interior-point methods | OPTIMAL-DESIGN | SIMULTANEOUS GATE | geometric programming | 2 RESTRICTIONS | SIMULTANEOUS BUFFER | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | generalized geometric programming | GLOBAL OPTIMIZATION | convex optimization | ELMORE DELAY | INVENTORY MODEL | SENSITIVITY ANALYSIS | Physicians (General practice) | Studies | Problems | Operations research

Journal Article

SIAM Journal on Imaging Sciences, ISSN 1936-4954, 09/2014, Volume 7, Issue 3, pp. 1724 - 1754

We present primal-dual decomposition algorithms for convex optimization problems with cost functions f(x) + g(Ax), where f and g have inexpensive proximal...

Douglasâ€“Rachford algorithm | Image deblurring | Monotone operators | Convex optimization | MATHEMATICS, APPLIED | SIGNAL RECOVERY | image deblurring | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | ALGORITHMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | ALTERNATING DIRECTION METHOD | PENALTY | Douglas-Rachford algorithm | MODELS | MONOTONE VARIATIONAL-INEQUALITIES | monotone operators | convex optimization | Operators | Splitting | Algorithms | Structured matrices | Images | Decomposition | Regularization | Optimization

Douglasâ€“Rachford algorithm | Image deblurring | Monotone operators | Convex optimization | MATHEMATICS, APPLIED | SIGNAL RECOVERY | image deblurring | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | ALGORITHMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | ALTERNATING DIRECTION METHOD | PENALTY | Douglas-Rachford algorithm | MODELS | MONOTONE VARIATIONAL-INEQUALITIES | monotone operators | convex optimization | Operators | Splitting | Algorithms | Structured matrices | Images | Decomposition | Regularization | Optimization

Journal Article

Systems & Control Letters, ISSN 0167-6911, 08/2013, Volume 62, Issue 8, pp. 605 - 612

We present a system identification method for problems with partially missing inputs and outputs. The method is based on a subspace formulation and uses the...

Subspace method | Nuclear norm | System identification | Hankel structure | Low-rank matrix approximation | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SUBSPACE MODEL IDENTIFICATION | REGULARIZATION | AUTOMATION & CONTROL SYSTEMS | Approximation | Mathematical analysis | Norms | Control systems | Subspaces | Standards | Optimization | TEKNIKVETENSKAP | Engineering and Technology | Teknik och teknologier | TECHNOLOGY

Subspace method | Nuclear norm | System identification | Hankel structure | Low-rank matrix approximation | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SUBSPACE MODEL IDENTIFICATION | REGULARIZATION | AUTOMATION & CONTROL SYSTEMS | Approximation | Mathematical analysis | Norms | Control systems | Subspaces | Standards | Optimization | TEKNIKVETENSKAP | Engineering and Technology | Teknik och teknologier | TECHNOLOGY

Journal Article

Statistics and Computing, ISSN 0960-3174, 7/2019, Volume 29, Issue 4, pp. 725 - 738

We consider T-optimal experiment design problems for discriminating multi-factor polynomial regression models where the design space is defined by polynomial...

Statistics and Computing/Statistics Programs | Semidefinite programming | Continuous design | Convex optimization | Artificial Intelligence | Equivalence theorem | Statistical Theory and Methods | Statistics | Moment relaxation | Probability and Statistics in Computer Science | DISCRIMINATION | STATISTICS & PROBABILITY | COMPUTER SCIENCE, THEORY & METHODS | Electrical engineering | Relaxation | Analysis | Methods

Statistics and Computing/Statistics Programs | Semidefinite programming | Continuous design | Convex optimization | Artificial Intelligence | Equivalence theorem | Statistical Theory and Methods | Statistics | Moment relaxation | Probability and Statistics in Computer Science | DISCRIMINATION | STATISTICS & PROBABILITY | COMPUTER SCIENCE, THEORY & METHODS | Electrical engineering | Relaxation | Analysis | Methods

Journal Article

SIAM Review, ISSN 0036-1445, 3/1996, Volume 38, Issue 1, pp. 49 - 95

In semidefinite programming, one minimizes a linear function subject to the constraint that an affine combination of symmetric matrices is positive...

Algorithms | Linear inequalities | Eigenvalues | Linear programming | Matrices | Polynomials | Mathematics | Control theory | Combinatorial optimization | Ellipsoids | Eigenvalue optimization | Semidefinite programming | Interior-point methods | Convex optimization | System and control theory | LINEAR COMBINATION | MATHEMATICS, APPLIED | interior-point methods | eigenvalue optimization | TRACE FACTOR-ANALYSIS | ALGORITHM | EQUATIONS | SYMMETRICAL MATRIX | LEAST-SQUARES | semidefinite programming | combinatorial optimization | LARGEST EIGENVALUES | LOWER BOUNDS | system and control theory | convex optimization | OPTIMIZATION | INDEFINITE SYSTEMS | Usage | Convex programming | Mathematical optimization | Analysis | Methods

Algorithms | Linear inequalities | Eigenvalues | Linear programming | Matrices | Polynomials | Mathematics | Control theory | Combinatorial optimization | Ellipsoids | Eigenvalue optimization | Semidefinite programming | Interior-point methods | Convex optimization | System and control theory | LINEAR COMBINATION | MATHEMATICS, APPLIED | interior-point methods | eigenvalue optimization | TRACE FACTOR-ANALYSIS | ALGORITHM | EQUATIONS | SYMMETRICAL MATRIX | LEAST-SQUARES | semidefinite programming | combinatorial optimization | LARGEST EIGENVALUES | LOWER BOUNDS | system and control theory | convex optimization | OPTIMIZATION | INDEFINITE SYSTEMS | Usage | Convex programming | Mathematical optimization | Analysis | Methods

Journal Article

SIAM Journal on Optimization, ISSN 1052-6234, 2014, Volume 24, Issue 2, pp. 873 - 897

Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general nonpolyhedral convex cones because the...

Semidefinite programming | Decomposition | Interior-point algorithms | semidefinite programming | MATHEMATICS, APPLIED | EXPLOITING SPARSITY | MATRICES | ALGORITHM | IMPLEMENTATION | decomposition | interior-point algorithms | INTERIOR-POINT METHODS | SDP | SEMIDEFINITE | Operators | Conics | Cones | Inequalities | Nonlinearity | Joining | Optimization

Semidefinite programming | Decomposition | Interior-point algorithms | semidefinite programming | MATHEMATICS, APPLIED | EXPLOITING SPARSITY | MATRICES | ALGORITHM | IMPLEMENTATION | decomposition | interior-point algorithms | INTERIOR-POINT METHODS | SDP | SEMIDEFINITE | Operators | Conics | Cones | Inequalities | Nonlinearity | Joining | Optimization

Journal Article

12.
Full Text
Sampling method for semidefinite programmes with non-negative Popov function constraints

International Journal of Control, ISSN 0020-7179, 02/2014, Volume 87, Issue 2, pp. 330 - 345

An important class of optimisation problems in control and signal processing involves the constraint that a Popov function is non-negative on the unit circle...

semidefinite programming | Kalman-Yakubovich-Popov lemma | Popov function constraint | linear matrix inequality | sampling method | OPTIMIZATION PROBLEMS | ROBUST STABILITY | TIME-INVARIANT SYSTEMS | ALGORITHMS | POLYNOMIALS | LMI CONDITION | COMPUTATION | LINEAR MATRIX INEQUALITIES | AUTOMATION & CONTROL SYSTEMS | Problems | Semidefinite programming | Algorithms | Equivalence | Mathematical analysis | Packages | Inequalities | Mathematical models | Linear matrix inequalities | Mathematical programming | Teknik och teknologier | TEKNIKVETENSKAP | Kalman-Yakubovich-Popov lemma; Popov function constraint; sampling method; semidefinite programming; linear matrix inequality | Engineering and Technology | TECHNOLOGY

semidefinite programming | Kalman-Yakubovich-Popov lemma | Popov function constraint | linear matrix inequality | sampling method | OPTIMIZATION PROBLEMS | ROBUST STABILITY | TIME-INVARIANT SYSTEMS | ALGORITHMS | POLYNOMIALS | LMI CONDITION | COMPUTATION | LINEAR MATRIX INEQUALITIES | AUTOMATION & CONTROL SYSTEMS | Problems | Semidefinite programming | Algorithms | Equivalence | Mathematical analysis | Packages | Inequalities | Mathematical models | Linear matrix inequalities | Mathematical programming | Teknik och teknologier | TEKNIKVETENSKAP | Kalman-Yakubovich-Popov lemma; Popov function constraint; sampling method; semidefinite programming; linear matrix inequality | Engineering and Technology | TECHNOLOGY

Journal Article

SIAM Review, ISSN 0036-1445, 3/2007, Volume 49, Issue 1, pp. 52 - 64

A sharp lower bound on the probability of a set defined by quadratic inequalities, given the first two moments of the distribution, can be efficiently computed...

Optimal solutions | Linear algebra | Discrete random variables | Chebyshevs inequality | Mathematical duality | Mathematical moments | Mathematical inequalities | Problems and Techniques | Random variables | Ellipses | Quadratic inequalities | Semidefinite programming | Duality theory | Moment problems | Convex optimization | Chebyshev inequalities | semidefinite programming | duality theory | MATHEMATICS, APPLIED | INEQUALITIES | moment problems | convex optimization | Chebyshev approximation | Algebras, Linear | Analysis | Tests, problems and exercises

Optimal solutions | Linear algebra | Discrete random variables | Chebyshevs inequality | Mathematical duality | Mathematical moments | Mathematical inequalities | Problems and Techniques | Random variables | Ellipses | Quadratic inequalities | Semidefinite programming | Duality theory | Moment problems | Convex optimization | Chebyshev inequalities | semidefinite programming | duality theory | MATHEMATICS, APPLIED | INEQUALITIES | moment problems | convex optimization | Chebyshev approximation | Algebras, Linear | Analysis | Tests, problems and exercises

Journal Article

Mathematical Programming, ISSN 0025-5610, 2018, Volume 179, Issue 1-2, pp. 85 - 108

The primal-dual hybrid gradient (PDHG) algorithm proposed by Esser, Zhang, and Chan, and by Pock, Cremers, Bischof, and Chambolle is known to include as a...

Douglasâ€“Rachford splitting | Primal-dual algorithms | Monotone operators | Proximal algorithms | MATHEMATICS, APPLIED | CONVERGENCE ANALYSIS | ALGORITHM | DECOMPOSITION | SUM | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MONOTONE INCLUSIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford splitting | OPTIMIZATION | Splitting | Algorithms

Douglasâ€“Rachford splitting | Primal-dual algorithms | Monotone operators | Proximal algorithms | MATHEMATICS, APPLIED | CONVERGENCE ANALYSIS | ALGORITHM | DECOMPOSITION | SUM | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MONOTONE INCLUSIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Douglas-Rachford splitting | OPTIMIZATION | Splitting | Algorithms

Journal Article

European Journal of Nuclear Medicine and Molecular Imaging, ISSN 1619-7070, 12/2018, Volume 45, Issue 13, pp. 2342 - 2357

To assess the binding of the PET tracer [18F]THK5351 in patients with different primary progressive aphasia (PPA) variants and its correlation with clinical...

Nonfluent variant | Medicine & Public Health | Agrammatism | Orthopedics | [ 18 F]THK5351 binding | Oncology | Tau | Nuclear Medicine | Imaging / Radiology | Cardiology | Primary progressive aphasia | Motor speech | F]THK5351 binding | MRI | ALZHEIMERS-DISEASE | APRAXIA | PATHOLOGY | POSITRON-EMISSION-TOMOGRAPHY | TRACER | F-18-THK5351 | IN-VIVO | HYPOMETABOLISM | [F-18]THK5351 binding | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | Quinolines - metabolism | Radioactive Tracers | Aphasia, Primary Progressive - metabolism | Humans | Middle Aged | Aged, 80 and over | Female | Male | Aged | Positron-Emission Tomography | Aminopyridines - metabolism | Aphasia, Primary Progressive - diagnostic imaging | Cortex (premotor) | Cerebellum | Neuroimaging | Brain | Basal ganglia | Mesencephalon | Impairment | Cortex (motor) | Substantia grisea | Proteins | Cortex (frontal) | Thalamus | Alzheimer's disease | Cortex (temporal) | Deoxyribonucleic acid--DNA | Supplementary motor area | Medical imaging | Statistical analysis | Neurodegenerative diseases | Brain mapping | Fluorine isotopes | Regression analysis | Patients | Postcentral gyrus | Ganglia | Pathology | Magnetic resonance imaging | Tau protein | Correlation analysis | Biomarkers | Aphasia | Positron emission tomography

Nonfluent variant | Medicine & Public Health | Agrammatism | Orthopedics | [ 18 F]THK5351 binding | Oncology | Tau | Nuclear Medicine | Imaging / Radiology | Cardiology | Primary progressive aphasia | Motor speech | F]THK5351 binding | MRI | ALZHEIMERS-DISEASE | APRAXIA | PATHOLOGY | POSITRON-EMISSION-TOMOGRAPHY | TRACER | F-18-THK5351 | IN-VIVO | HYPOMETABOLISM | [F-18]THK5351 binding | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | Quinolines - metabolism | Radioactive Tracers | Aphasia, Primary Progressive - metabolism | Humans | Middle Aged | Aged, 80 and over | Female | Male | Aged | Positron-Emission Tomography | Aminopyridines - metabolism | Aphasia, Primary Progressive - diagnostic imaging | Cortex (premotor) | Cerebellum | Neuroimaging | Brain | Basal ganglia | Mesencephalon | Impairment | Cortex (motor) | Substantia grisea | Proteins | Cortex (frontal) | Thalamus | Alzheimer's disease | Cortex (temporal) | Deoxyribonucleic acid--DNA | Supplementary motor area | Medical imaging | Statistical analysis | Neurodegenerative diseases | Brain mapping | Fluorine isotopes | Regression analysis | Patients | Postcentral gyrus | Ganglia | Pathology | Magnetic resonance imaging | Tau protein | Correlation analysis | Biomarkers | Aphasia | Positron emission tomography

Journal Article

Mathematical Methods of Operations Research, ISSN 1432-2994, 2/2017, Volume 85, Issue 1, pp. 19 - 41

We analyze the proximal Newton method for minimizing a sum of a self-concordant function and a convex function with an inexpensive proximal operator. We...

Proximal Newton method | Calculus of Variations and Optimal Control; Optimization | Self-concordance | Convex optimization | Mathematics | Operation Research/Decision Theory | Business and Management, general | Covariance selection | Chordal sparsity | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | Computer science | Electrical engineering | Algorithms | Analysis | Methods | Studies | Operations research | Optimization | Matrices (mathematics) | Mathematical analysis | Newton methods | Mathematical models | Inverse | Convergence

Proximal Newton method | Calculus of Variations and Optimal Control; Optimization | Self-concordance | Convex optimization | Mathematics | Operation Research/Decision Theory | Business and Management, general | Covariance selection | Chordal sparsity | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | Computer science | Electrical engineering | Algorithms | Analysis | Methods | Studies | Operations research | Optimization | Matrices (mathematics) | Mathematical analysis | Newton methods | Mathematical models | Inverse | Convergence

Journal Article

SIAM Journal on Optimization, ISSN 1052-6234, 2006, Volume 16, Issue 4, pp. 939 - 964

We present a new semidefinite programming formulation of sum-of-squares representations of nonnegative polynomials, cosine polynomials, and trigonometric...

Nonnegative polynomials | Semidefinite programming | Interior-point methods | semidefinite programming | MATHEMATICS, APPLIED | OPTIMIZATION PROBLEMS | nonnegative polynomials | interior-point methods

Nonnegative polynomials | Semidefinite programming | Interior-point methods | semidefinite programming | MATHEMATICS, APPLIED | OPTIMIZATION PROBLEMS | nonnegative polynomials | interior-point methods

Journal Article

SIAM Journal on Optimization, ISSN 1052-6234, 2017, Volume 27, Issue 3, pp. 1362 - 1389

This paper presents generalizations of semidefinite programming formulations of 1 norm optimization problems over infinite dictionaries of vectors of complex...

Atomic norm | Kalman-Yakubovich-Popov lemma | Semidefinite programming | Matrix pencils | semidefinite programming | MATHEMATICS, APPLIED | PENCIL METHOD | matrix pencils | OPTIMIZATION | SUM | PARAMETERS | atomic norm

Atomic norm | Kalman-Yakubovich-Popov lemma | Semidefinite programming | Matrix pencils | semidefinite programming | MATHEMATICS, APPLIED | PENCIL METHOD | matrix pencils | OPTIMIZATION | SUM | PARAMETERS | atomic norm

Journal Article