## 1 Introduction
else Skip to Step 4. end if Update the target area noise reduction set \(\mathbf{NR}_{\_}{\gamma_{n}}\) and the constraint point noise reduction set \(\mathbf{NR}_{\_}{\_}{\text{c},\gamma_{\_}{\gamma_{\_}{\gamma_{\_}{\gamma_{\_}{ \gamma_{\_}{\gamma}}}}}}\) end for Step 4: Obtain the maximum target area noise reduction \(NR_{\_}{\text{max}}=\text{max}(\mathbf{NR}_{\_}{\gamma_{\_}{\gamma_{\_}{\gamma_{ \_}{\gamma_{\_}{\gamma}}}}})\). Step 5: Initialize the alternative sparse penalty parameter set \(\mathbf{\gamma}_{\_}{a}\) and the alternative constraint point noise reduction set \(\mathbf{NR}_{\_}{\text{c},\gamma_{\_}{\gamma_{\_}{\gamma_{\_}{\gamma}}}}\), so that their elements are 0. Initialize a small value of noise reduction \(\Delta_{NR}\). Step 6: for \(\text{a}=1,2,\ldots,\text{length}(\mathbf{NR}_{\_}{\gamma_{\_}{\gamma_{\_}{ \gamma}}})\) if \(NR_{\_}{\gamma_{\_}{\gamma_{\_}{\gamma}}}\geq NR_{\_}\text{max}-\Delta_{NR}\) Update the alternative sparse penalty parameter set \(\mathbf{\gamma}_{a}\) and the alternative con-straint point noise reduction set \(\mathbf{NR}_{\_}{\text{c},\gamma_{\_}{\gamma_{\_}{\gamma_{\_}{\gamma_{\_}{\gamma_{ \_}{\gamma_{\_}{\gamma_{\_}{\gamma_{\_{\_}}}}}}}}}}\). end if end for Step 7: Obtain the maximum constraint point noise reduction \(NR_{\_}{\text{c},\text{0}}=\text{max}(\mathbf{NR}_{\_}{\text{c},\gamma_{\_}{ \gamma_{\_}{\gamma_{\_}{\gamma_{\_}{\gamma_{\_}{\gamma}}}}}})\). Step 8: Select the sparse penalty parameter \(\gamma_{\_}{a}\) corresponding to \(NR_{\_}{\text{c},\text{0}}\) as the final sparse penalty parameter \(\gamma_{\_}{\text{CLASSO}}\). Step 9: Calculate the strength vector of \(NL\) optimized secondary loudspeakers \(\mathbf{q}_{\_}{\text{s},\_7 CLASSO}\) using Equation (6). ```  
**Algorithm 1** The CLASSO-RLS algorithm  
In this paper, the proposed CLASSO-RLS algorithm is compared with the RLS algorithm and the previous LASSO-RLS algorithm [14; 15; 16; 17; 20]. The LASSO-RLS algorithm often selects sparse penalty parameter \(\gamma_{\_}{\text{CLASSO}}\) using cross-validation techniques [14]. When \(NL\) secondary loudspeakers are chosen, the sparse penalty parameter can be selected in two ways. The first approach [14] is to assign the empirical value \(\left.\gamma_{\_}{n\text{c}}\right\|=\left(\frac{1}{20}\right)\left\|\mathbf{Z} _{left}\mathbf{Z}_{right}\mathbf{q}_{p}\mathbf{q}_{p}\right\|_{\_}{\infty}\) advocated in reference [28] to the sparse penalty parameter, and subsequently use the BCD algorithm [14] to solve Equation (7) and obtain the solution \(\mathbf{q}_{\_}{\text{s}}\). Consequently, the secondary loudspeakers with the \(NL\) largest intensity values are selected as the optimized secondary loudspeakers. In the simulation, the first approach is called LASSO-RLS-method. The second method [20] is to increase \(\gamma_{LASSO}\) and use the BCD method to solve Equation (7) until the number of non-zero entries in the strength vector of the optimized secondary loudspeakers is \(NL\). Finally, the \(NL\) secondary loudspeakers are selected as the optimized secondary loudspeakers. In the simulation, this method is called the LASSO-RLS-\(\gamma_{NL}\) algorithm. Neither the LASSO-RLS-\(\gamma_{\text{C}}\) method nor LASSO-RLS-\(\gamma_{NL}\) algorithm have constraint points, which is the biggest difference to the proposed CLASSSO-RLS algorithm. Both the LASSO-RLS-\(\gamma_{\text{C}}\) method and LASSO-RLS-\(\gamma_{NL}\) algorithm have two stages. In the first stage, \(NL\) optimized secondary loudspeakers are selected from \(NS\) candidate secondary loudspeakers. In the second stage, \(\mathbf{q}_{s\_7 LASSO}\) is solved using Equation (6).