Journal: Frontiers in Human Neuroscience

Article Title: Lattice layout and optimizer effect analysis for generating optimal transcranial electrical stimulation (tES) montages through the metaheuristic L1L1 method

doi: 10.3389/fnhum.2024.1201574

Figure Lengend Snippet: Description of the Linear Programming (LP) solvers applied for solving the L1L1 optimization problem through the Interior-Point (IP), Primal-Simplex (PS), and Dual-Simplex (DS) algorithms.

Article Snippet: We tested the L1L1 method using the commercial solvers of MOSEK Optimization Suite (Release 9) (Mosek, ) and Gurobi Optimization (9.5.1) (Gurobi Optimization LLC, ), and compared them to the open-source alternatives (Grant and Boyd, ) SDPT3 (4.0) (Tütüncü et al., ) and SeDuMi (1.3.5) (Sturm, ; Frenk et al., ; Polik et al., ) as well as Matlab R2020b's (MathWorks) Interior-Point-Legacy (IPL) algorithm, which originates from the open LIPSOL (Zhang, ) toolbox.

Techniques:

Journal: Frontiers in Human Neuroscience

Article Title: Lattice layout and optimizer effect analysis for generating optimal transcranial electrical stimulation (tES) montages through the metaheuristic L1L1 method

doi: 10.3389/fnhum.2024.1201574

Figure Lengend Snippet: Performance comparison of the exhaustive search for solving the L1-norm fitted and penalized (L1L1) optimization method with current density Γ as the objective function. The coarse (A) search space κ = 15 produces 225 evaluations, and the finer (B) search space κ = 40 with 1600 evaluations, both using regularization parameter α (x-axis) and the nuisance threshold level ε (y-axis). The candidate solutions with respect to current density Γ max and focality Θ max are marked with a yellow and purple star, respectively. The maximizers are generally found around from area in which α is between −71 to −50 dB dB (decibels) and ε from 0 to −98 dB. Notice that in the case of using the Gurobi package, with a Simplex algorithm, both optimal candidate solutions for either a stimulus focality or a current density both optimal solutions are taking the same ( α , ε ) tuning parameters due to the sharp steepness from the coarse search space. The volumetric current density on every chart is given in Amperes per square meter (A/m 2 ).

Article Snippet: We tested the L1L1 method using the commercial solvers of MOSEK Optimization Suite (Release 9) (Mosek, ) and Gurobi Optimization (9.5.1) (Gurobi Optimization LLC, ), and compared them to the open-source alternatives (Grant and Boyd, ) SDPT3 (4.0) (Tütüncü et al., ) and SeDuMi (1.3.5) (Sturm, ; Frenk et al., ; Polik et al., ) as well as Matlab R2020b's (MathWorks) Interior-Point-Legacy (IPL) algorithm, which originates from the open LIPSOL (Zhang, ) toolbox.

Techniques: Comparison