reviews: 
Comments: The paper takes several well-known ideas, in particular maximization/minimization over a continuous $x$ in a discrete problem, and what the paper calls block-search strategy (a.k.a. top-k). These approaches are used to simultaneously find the minimum or maximum of a CP-tensor. Several theorems in the paper do not fully shed light on the accuracy of the method, the evaluation of which remains more empirical. Numerical experiments are set on random low-dimensional CP-tensors, CP-factorization of two well-known model fucntions, and CP-factorization of several small real-world datasets.
Strengths: - The paper is generally well structured and written
- In some cases good results are obtained when searching for CP-tensors minimum
Weaknesses: - The paper takes known algorithms, and only connects them together in the special case of the problem of finding the extremum of CP-tensors.
 
- Comparisons in numerical examples are given with only two (and in the case of finding the minimum, only one) other method, which is clearly insufficient.
   * The coloring in the tables when both the presented method and its competitor are the best is given only for the presented method. It would be fair to color all cases when a particular method was the best. For example, in Table 2, color all cases of minimum for both functions, since they are equal for the presented method and for MInCPD. 

- Table 1, which compares methods for random vectors, is not entirely honest. Indeed, the _star sampling_ method can only find maximum (modulo) elements of CP-tensor. But once one is found, let its values be $m$, we can do a transformation $m \mathcal E - \mathcal A$ (very similar to the one described on page 2 in section 2 of the paper), which increases the CP-rank by only 1. Then the problem of finding the minimum in the initial tensor $\mathcal A$ reduces to finding the maximum in this tensor. Unfortunately, I haven't found open source code for the _star sampling_ method, but I suspect it would work (with this trick) just as well as the presented method. And in the problem of maximum finding the _star sampling_ algorithm, as the authors honestly write, already wins, so the the contribution made by this new approach may be considered negligible in this case.

- As for finding optima of the Rastrigin and Schwefel model functions, this and many other functions were used to test a similar algorithm optima_tt, which is cited in this paper as Chertkov et al. (2022). If we take the _optima_tt_ code, which is open source, and apply it to TT-tensors that exactly describe the two functions (with exact TT-ranks of 2 each) with the same parameters (n=4096, d=10), we get the following results for the minimum and for the maximum (I took the hyperparameter $k=5$):
Rastrigin: min: 0.0014192582... max: 403.5327475...
Schwefel min: 0.000725485....  max: 8379.65727....
Thus, for these two functions the combination of using CP-compression and the newly presented method is meaningless.

- No code is provided so that experiments can be repeated

- The Theorems in the paper are rather trivial, one of them is not proved at all (see below). Thus, there is no serious analysis of convergence. To be fair, it should be noted that there is no such analysis for many other similar methods.

- in the proof of Theorem 1, in the last equation in (A.1) it is not clear what "$x^{(n)}=1$" means. If it is a constant vector, how can we search for $\max$ w.r.t. it?
If it $\||x^{(n)}\||_2=1$ then (A.1) is not just equivalent (as the proof of the theorem states), but coincides with problem (2.3). 
But Theorem 1 asserts more than that. It asserts that for continuous values of $x^{(n)}$, i.e., $x^{(n)}\in\mathbb R^{I_n}$, the solution of the maximization problem (2.3) coincides with the maximum of CP-Tensor element, i.e., with the case where each vector $x^{(n)}$ are binary and represents (different) rows of the unit matrix. In this form, Theorem 1 has never been proved in the this paper.

- times in the Table 4 with experiments with "real-world" data are not relevant, because it will be much faster, for example, for COVID dataset expand it the full tensor, and then search the maximum. Moreover, the compression time of these real-world datasets into CP format is not taken into account.
    * link the mnist dataset is not valid -- login and password requires to access it.

- at the beginning (page 3) the paper says that the algorithm parameter-free. But then it turns out that the final Algorithm has an adjustable parameter $b$.

Minor:

Suggestion:  put brackets around formula references (use "\eqref" instead of "\ref").
Recommendation: 1: strong reject
Reviewer confidence: 4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
Soundness/correctness: 3 good
Clarity: 3 good