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Is there a function in R that does optimization with quadratic constraints?
Reference: http://en.wikipedia.org/wiki/Quadratically_constrained_quadratic_program
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Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize (minimize or maximize) a multivariate quadratic function subject to linear constraints on the variables.
Mixed-integer quadratic programming (MIQP) is the problem of optimizing a quadratic function. over points in a polyhedral set that have some components integer, and others continuous.
Quadratic programming (QP) is the problem of optimizing a quadratic objective function and is one of the simplests form of non-linear programming. 1 The objective function can contain bilinear or up to second order polynomial terms,2 and the constraints are linear and can be both equalities and inequalities.
You should look through your options at the CRAN Optimization and Mathematical ProgrammingTask View.
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Yes, there are several software packages that can solve QCQPs.
CLSOCP solves SOCP problems. DWD also solves SOCP problems. Rcsdp solves SDP problems.
Keep in mind that
QCQPs are a subset of SOCPs, which in turn are a subset of SDPs.
There are references online illustrating how to formulate a QCQP as an SOCP or SDP
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