CODEWITHSUNDEEP
rmathematical-optimization
user236215
user236215

Reputation: 7546

Quadratically constrained quadratic programming in R

Is there a function in R that does optimization with quadratic constraints?

Reference: http://en.wikipedia.org/wiki/Quadratically_constrained_quadratic_program

Upvotes: 6

Views: 3856

Answers (3)

Silverfish
Silverfish

Reputation: 1954

From the CRAN page for the optiSolve package: https://cran.r-project.org/web/packages/optiSolve/optiSolve.pdf

The following steps are included in solving a constrained optimization problem (cop):

  1. Define the objective with one of the following functions: linfun defines a linear objective function, quadfun defines a quadratic objective function, ratiofun defines a rational objective function.
  2. Define the constraints by using the following functions: lincon defines linear equality and inequality constraints, quadcon defines quadratic constraints, ratiocon defines rational constraints, lbcon defines lower bounds for the variables, ubcon defines upper bounds for the variables.
  3. Put the objective function and the constraints together to define the optimization problem: cop defines a constrained optimization problem.
  4. Solve the optimization problem: solvecop solves a constrained optimization problem.
  5. Check if the solution fulfils all constraints: validate checks if the solution fulfils all constraints, and calculates the values of the constraints.

So a quadratically constrained quadratic objective requires you to use quadfun with quadcon.

You could also use slsqp in the nloptr package. This is one of the methods that optiSolve can call. https://cran.r-project.org/web/packages/nloptr/nloptr.pdf

Upvotes: 0

Erwin Kalvelagen
Erwin Kalvelagen

Reputation: 16724

All these answer seem to forget one important thing: the solver to use depends heavily on whether the constraint is convex or not. If convex we can use readily available QCP / SOCP solvers (including Cplex and Gurobi). If not convex, we can try a general purpose NLP solver (such as IPOPT). Non-convex global solvers are another possibility, but most are not directly available under R.

Upvotes: 0

MichaelJ
MichaelJ

Reputation: 217

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

Upvotes: 3

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