SDPmeanP

SDPmeanP is a term that appears in the optimization literature as a shorthand for a class of problems that combine semidefinite programming (SDP) with mean-preserving constraints or projections. The exact definition of SDPmeanP is not standardized and the interpretation can vary across sources, making it more of a descriptive label than a single fixed algorithm.

In its broadest sense, SDP refers to convex optimization problems of the form minimize Tr(CX) subject to X being positive semidefinite and satisfying a set of linear constraints. When SDPmeanP is used, it typically adds a linear mean-preservation requirement, which enforces that certain linear functions of X equal a specified mean value. Conceptually, this can be viewed as projecting a data matrix or decision variable onto the intersection of the positive semidefinite cone and a linear subspace defined by mean constraints.

Computationally, these problems remain convex when the mean constraints are linear, and they can be solved by standard SDP solvers or interior-point methods. The complexity grows polynomially with problem size, but practical limits arise for high-dimensional instances. Exploiting problem structure, such as sparsity or symmetry, can improve scalability.

Applications of SDPmeanP concepts are found in areas where one wishes to enforce global structured quantities (means) while maintaining PSD feasibility. Potential domains include clustering and community detection, graph embedding, covariance estimation, and certain forms of dimensionality reduction or signal processing where mean information is known or desired.

Because SDPmeanP is not a single, canonical formulation, users should consult the context in which the term is used to understand the precise constraints and objectives. See also semidefinite programming, convex optimization, and projection methods.