On the Implementation and Usage of SDPT3 – A Matlab Software Package for Semidefinite-Quadratic-Linear Programming, Version 4.0

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

doi:10.1007/978-1-4614-0769-0_25

Cited by 173 publications

(182 citation statements)

References 36 publications

(47 reference statements)

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“…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

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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.

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Section: Implementation Detailsmentioning

confidence: 99%

Robust Growth-Optimal Portfolios

2016

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“…We take advantage of the connection of the penalized likelihood and the the the maxdeterminant optimization problem (Vanderberghe et al, 1996). We make use of the SDPT3 algorithm (Toh, 2006) to manage higher dimensional problems. We consider the optimization problem:…”

Section: Max Determinant Optimization Problemmentioning

confidence: 99%

Dynamic Gaussian Graphical Models for Modelling Genomic Networks

Abbruzzo

Serio

Wit

2014

Computational Intelligence Methods for Bioinformatics and Biostatistics

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Abstract. After sequencing the entire DNA for various organisms, the challenge has become understanding the functional interrelatedness of the genome. Only by understanding the pathways for various complex diseases can we begin to make sense of any type of treatment. Unfortunately, decyphering the genomic network structure is an enormous task. Even with a small number of genes the number of possible networks is very large. This problem becomes even more difficult, when we consider dynamical networks. We consider the problem of estimating a sparse dynamic Gaussian graphical model with L1 penalized maximum likelihood of structured precision matrix. The structure can consist of specific time dynamics, known presence or absence of links in the graphical model or equality constraints on the parameters. The model is defined on the basis of partial correlations, which results in a specific class precision matrices. A priori L1 penalized maximum likelihood estimation in this class is extremely difficult, because of the above mentioned constraints, the computational complexity of the L1 constraint on the side of the usual positive-definite constraint. The implementation is non-trivial, but we show that the computation can be done effectively by taking advantage of an efficient maximum determinant algorithm developed in convex optimization.

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“…All implementations have been carried out in MATLAB R2010b using YALMIP [Löf04] and the solver SDPT3 [TTT10] with default settings unless otherwise specified. The computations have been run on an Intel Core i5 CPU M 250 4 GHz with 4 GB of RAM.…”

Section: Identification Of Frequency Domain Power Spectramentioning

confidence: 99%

“…In particular, several general-purpose packages now exploit low-rank structure in the coefficient matrices of SDPs, in addition to sparsity. For example, SDPT3 [TTT10] offers this capability [FLH11]. Some of the fast algorithms for SDPs involving nonnegative scalar polynomials and Popov functions [LP04, RV06, RDV07, LV07] are based on exploiting low-rank structure and are are therefore easily implemented with a general-purpose solver that exploits such structure.…”

Section: Introductionmentioning

confidence: 99%

Sampling method for semidefinite programmes with non-negative Popov function constraints

Hansson

Vandenberghe

2013

International Journal of Control

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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 or the imaginary axis. Such a constraint is convex in the coefficients of the Popov function. It can be converted to a finite-dimensional linear matrix inequality via the Kalman-Yakubovich-Popov lemma. However, the linear matrix inequality reformulation requires an auxiliary matrix variable and often results in a very large semidefinite programming problem. Several recently published methods exploit problem structure in these semidefinite programmes to alleviate the computational cost associated with the large matrix variable. These algorithms are capable of solving much larger problems than general-purpose semidefinite programming packages. In this paper, we address the same problem by presenting an alternative to the linear matrix inequality formulation of the non-negative Popov function constraint. We sample the constraint to obtain an equivalent set of inequalities of low dimension, thus avoiding the large matrix variable in the linear matrix inequality formulation. Moreover, the resulting semidefinite programme has constraints with low-rank structure, which allows the problems to be solved efficiently by existing semidefinite programming packages. The sampling formulation is obtained by first expressing the Popov function inequality as a sum-of-squares condition imposed on a polynomial matrix and then converting the constraint into an equivalent finite set of interpolation constraints. A complexity analysis and numerical examples are provided to demonstrate the performance improvement over existing techniques

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On the Implementation and Usage of SDPT3 – A Matlab Software Package for Semidefinite-Quadratic-Linear Programming, Version 4.0

Cited by 173 publications

References 36 publications

Robust Growth-Optimal Portfolios

Robust Growth-Optimal Portfolios

Dynamic Gaussian Graphical Models for Modelling Genomic Networks

Sampling method for semidefinite programmes with non-negative Popov function constraints

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