Sieve-SDP ([1]) is a preprocessing algorithm for semidefinite programming of the form min. <C, X> s.t. A(X) == b X in K where K is the direct product of R^p, R^q_+ and S^r_+ (Euclidean space, nonnegative orthant, and positive semidefinite cones). It is a MATLAB-based software. For detail, call >> help SieveSDP; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% HOW TO FORMULATE A PROBLEM %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The input/output format of Sieve-SDP is Mosek Matlab format ([2, Section 9.7]). To load a problem ``problem.mat” in Matlab, call >> prob = load(‘problem.mat’); If the problem is stored in a different formats supported by Mosek, e.g., Task format, call >> [~, res] = mosekopt(['read(problem.task.gz)']); >> prob = res.prob; in order to convert the problem to Mosek Matlab format. To convert it back, call >> mosekopt(['min write(problem.task.gz)'], prob); If the problem is stored in SeDuMi format ([4]), call >> prob = convert_sedumi2mosek(problem_A, problem_b, problem_c, problem_K); in order to convert the problem to Mosek Matlab format. To convert it back, call >> [problem_A, problem_b, problem_c, problem_K] = convert_mosek2sedumi(prob); The folder “test examples” contains 9 datasets saved as .zip files. After unzipping a dataset, you will see SDP problems saved as .mat files. They are already in Mosek Matlab format, which is Sieve-SDP input/output format. They are SDP relaxations of polynomial optimization problems from [6] generated by Gloptipoly 3 ([7]), as one of the datasets tested in [1]. Other datasets tested in [1] include [8] and … %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% HOW TO PREPROCESS A PROBLEM USING SIEVE-SDP %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% To preprocess a problem using SieveSDP, call >> [probr, info] = SieveSDP(prob); If info.infeasible == 1, then problem is infeasible. Otherwise, to solve a reduced problem by Mosek, call >> [rcode, res] = mosekopt(‘minimize’, probr); The problem solution is saved in ‘res’, c.f. [2]. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% HOW TO RECOVER ORIGINAL SOLUTION %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% If solution of original (before-preprocessed) problem is desired, call >> [x_original, X_original] = recoveryPrimal(res, info); where ‘info’ is an output from the call SieveSDP, ‘x_original’ corresponds to linear variables, and ‘X_original’ corresponds to PSD variables. If solution of original dual problem max. <b, y> s.t. A^* (y) + Z = C Z in K^* is desired, set >> option.DR = 1; and call SieveSDP by >> [probr, info] = SieveSDP(prob, option); After solving the problem by Mosek, call [y_original, z_original, Z_original, info1] = recoveryDual(res, info); Dual recovery may not always succeed ([5]). Its success status is saved in ‘info1’. ———- [1] Y. Zhu, G. Pataki, TD Quoc. Sieve-SDP: a simple facial reduction algorithm to preprocess semidefinite programs. Mathematical Programming Computation 11.3 (2019): 503-586. [2] http://docs.mosek.com/7.0/toolbox/A_guided_tour.html [3] http://docs.mosek.com/8.1/matlabfusion/supported-file-formats.html [4] http://sedumi.ie.lehigh.edu/sedumi/files/sedumi-downloads/SeDuMi_Guide_11.pdf [5] G. Pataki. Bad semidefinite programs: they all look the same[J]. SIAM Journal on Optimization, 2017, 27(1): 146-172. [6] Mareike Dressler, Sadik Iliman, and Timo de Wolff. An approach to constrained polynomial optimization via nonnegative circuit polynomials and geometric programming. Journal of Symbolic Computation, 2018. [7] http://homepages.laas.fr/henrion/software/gloptipoly/ [8] http://plato.asu.edu/ftp/sdp/