SDPT3 — A Matlab software package for semidefinite programming, Version 1.3

Toh, Kim-Chuan; Todd, Michael J.; Tütüncü, Reha

doi:10.1080/10556789908805762

Cited by 1,692 publications

(1,151 citation statements)

References 13 publications

Supporting

Mentioning

1,131

Contrasting

Unclassified

Order By: Relevance

“…(19) can be solved fast, using a variety of established solvers. The solver used in this work was SDPT3 (22), which was interfaced by YALMIP (23).…”

Section: Constrained Optimization and Reduction Of Its Complexitymentioning

confidence: 99%

Optimal design of multiple‐channel RF pulses under strict power and SAR constraints

Brunner

Pruessmann

2010

Magnetic Resonance in Med

View full text Add to dashboard Cite

Parallel radio frequency transmission has recently been explored as a means of tailoring the spatial response of MR excitation. In particular, parallel transmission is increasingly used to accelerate radio frequency pulses that rely on time-varying gradient fields to achieve selectivity in multiple dimensions. The design of the underlying multiple-channel radio frequency waveforms is mostly based on regularized least-squares optimization in close analogy with image reconstruction in parallel imaging. However, this analogy has important limitations. Unlike image reconstruction, the design of radio frequency waveforms is subject to multiple strict constraints, which arise from technical power limits, as well as safety limits on local and global energy deposition in vivo. To optimize excitation profiles under such strict constraints, it is proposed to depart from the regularization strategy and rely on semidefinite programming instead. To render this approach fast, it is performed in a reduced search space, which is obtained by initial Lanczos iteration. The proposed algorithm is demonstrated to enable efficient pulse optimization within exactly the given constraints, including local specific absorption rate limits for multiple compartments. It is also shown that the proposed approach readily accommodates advanced forward models of the excitation process, including the effects of local off-resonance and transverse relaxation.

show abstract

“…(19) can be solved fast, using a variety of established solvers. The solver used in this work was SDPT3 (22), which was interfaced by YALMIP (23).…”

Section: Constrained Optimization and Reduction Of Its Complexitymentioning

confidence: 99%

Optimal design of multiple‐channel RF pulses under strict power and SAR constraints

Brunner

Pruessmann

2010

Magnetic Resonance in Med

View full text Add to dashboard Cite

show abstract

“…Yalmip, [17] with SDPT3, [18]. The symmetric matrix H(x, λ, µ, δ) is a positive definite approximation of the Hessian of Φ c (x, λ, µ).…”

Section: Calculating the Search Directionmentioning

confidence: 99%

A partially augmented Lagrangian method for low order H-infinity controller synthesis using rational constraints

Ankelhed

Helmersson

Hansson

2011

IEEE Conference on Decision and Control and European Control Conference

View full text Add to dashboard Cite

When designing robust controllers, H-in nity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These problems become very complex, even when the order of the system is low. The approach used in this work is based on formulating the constraint on the maximum order of the controller as a polynomial (or rational) equation. This equality constraint is added to the optimization problem of minimizing an upper bound on the H-in nity norm of the closed loop system subject to linear matrix inequality (LMI) constraints. The problem is then solved by reformulating it as a partially augmented Lagrangian problem where the equality constraint is put into the objective function, but where the LMIs are kept as constraints. The proposed method is evaluated together with two well-known methods from the literature. The results indicate that the proposed method has comparable performance in most cases, especially if the synthesized controller has many parameters, which is the case if the system to be controlled has many input and output signals. Abstract-When designing robust controllers, H-infinity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the (augmented) system, the problem becomes nonconvex and it is relatively hard to solve. These problems become very complex, even when the order of the system is low.The approach used in this work is based on formulating the constraint on the maximum order of the controller as a polynomial (or rational) equation. This equality constraint is added to the optimization problem of minimizing an upper bound on the H-infinity norm of the closed loop system subject to linear matrix inequality (LMI) constraints. The problem is then solved by reformulating it as a partially augmented Lagrangian problem where the equality constraint is put into the objective function, but where the LMIs are kept as constraints.The proposed method is evaluated together with two wellknown methods from the literature. The results indicate that the proposed method has comparable performance in most cases, especially if the synthesized controller has many parameters, which is the case if the system to be controlled has many input and output signals.

show abstract

“…The version of SDPT3 used in our experiment is 4.0. Further information about SDPT3 can be found in Toh et al [50] and Toh et al [49] SDPT3 can be downloaded from http://www.math.nus.edu.sg/~mattohkc/sdpt3.html.…”

Section: Implementation Detailsmentioning

confidence: 99%

Robust Growth-Optimal Portfolios

2016

View full text Add to dashboard Cite

A portfolio which has a maximum expected growth rate is often referred to in the literature as a logoptimal portfolio or a growth-optimal portfolio. The origin of the log-optimal portfolio is arguably due to Kelly [27] when he observed that logarithmic wealth is additive in sequential investments and invented a betting strategy for gambling that relies on results from information theory. As a result of the law of large numbers, if investment returns are serially independent and identically distributed, the growth rate of any constant rebalanced portfolio (the log-optimal portfolio included) converges to its expectation. Moreover, under such conditions, one of the strongest advantages of the logoptimal portfolio is that, when implemented repeatedly, the log-optimal portfolio outperforms any other causal portfolio in the long run with probability 1. In other words, if all of these conditions are met, there is no sequence of portfolios that has a higher growth rate than that of the log-optimal portfolio. Stock markets however are different from casinos in the sense that investment returns are not serially independent and identically distributed. Also, since trading incurs transaction costs, investors are discouraged from making frequent trades. Plus, the probability distribution of stock returns is never precisely known, which impedes the calculation of the log-optimal portfolio. In this project, we generalize the results for the log-optimal portfolio. In particular, we establish similar guarantees for finite investment horizons where the distribution of stock returns is ambiguous.By focusing on constant rebalanced portfolios, we exploit temporal symmetries to formulate the emerging distributionally robust optimization problems as tractable conic programs whose sizes are independent of the investment horizon.

show abstract

SDPT3 — A Matlab software package for semidefinite programming, Version 1.3

Cited by 1,692 publications

References 13 publications

Optimal design of multiple‐channel RF pulses under strict power and SAR constraints

Optimal design of multiple‐channel RF pulses under strict power and SAR constraints

A partially augmented Lagrangian method for low order H-infinity controller synthesis using rational constraints

Robust Growth-Optimal Portfolios

Contact Info

Product

Resources

About