  # SCIP

Solving Constraint Integer Programs

cons_soc.h File Reference

## Detailed Description

constraint handler for second order cone constraints $$\sqrt{\gamma + \sum_{i=1}^{n} (\alpha_i\, (x_i + \beta_i))^2} \leq \alpha_{n+1}\, (x_{n+1}+\beta_{n+1})$$

Definition in file cons_soc.h.

#include "scip/def.h"
#include "scip/type_cons.h"
#include "scip/type_misc.h"
#include "scip/type_nlp.h"
#include "nlpi/type_nlpi.h"
#include "scip/type_retcode.h"
#include "scip/type_scip.h"
#include "scip/type_var.h"

Go to the source code of this file.

## Functions

SCIP_EXPORT SCIP_RETCODE SCIPincludeConshdlrSOC (SCIP *scip)

Second Order Cone Constraints

This constraint handler implements second order cone constraints of the form

$\sqrt{\gamma + \sum_{i=1}^{n} (\alpha_i\, (x_i + \beta_i))^2} \leq \alpha_{n+1}\, (x_{n+1}+\beta_{n+1})$

Here, $$\gamma \geq 0$$ and either $$x_{n+1} \geq -\beta_{n+1}, \alpha_{n+1} \geq 0$$ or $$x_{n+1} \leq -\beta_{n+1}, \alpha_{n+1} \leq 0$$.

Constraints are enforced by separation, where cuts are generated by linearizing the (convex) nonlinear function on the left-hand-side of the constraint. Further, a linear outer-approximation (which includes new variables) based on Ben-Tal & Nemirovski or Glineur can be added. See also

Timo Berthold and Stefan Heinz and Stefan Vigerske
Extending a CIP framework to solve MIQCPs
In: Jon Lee and Sven Leyffer (eds.), Mixed-integer nonlinear optimization: Algorithmic advances and applications, IMA volumes in Mathematics and its Applications, volume 154, 427-444, 2012.
On Polyhedral Approximations of the Second-order Cone
Mathematics of Operations Research 26:2, 193-205, 2001
François Glineur
Computational experiments with a linear approximation of second order cone optimization
Technical Report 2000:1, Faculté Polytechnique de Mons, Belgium
SCIP_EXPORT SCIP_RETCODE SCIPcreateConsSOC (SCIP *scip, SCIP_CONS **cons, const char *name, int nvars, SCIP_VAR **vars, SCIP_Real *coefs, SCIP_Real *offsets, SCIP_Real constant, SCIP_VAR *rhsvar, SCIP_Real rhscoeff, SCIP_Real rhsoffset, SCIP_Bool initial, SCIP_Bool separate, SCIP_Bool enforce, SCIP_Bool check, SCIP_Bool propagate, SCIP_Bool local, SCIP_Bool modifiable, SCIP_Bool dynamic, SCIP_Bool removable)

SCIP_EXPORT SCIP_RETCODE SCIPcreateConsBasicSOC (SCIP *scip, SCIP_CONS **cons, const char *name, int nvars, SCIP_VAR **vars, SCIP_Real *coefs, SCIP_Real *offsets, SCIP_Real constant, SCIP_VAR *rhsvar, SCIP_Real rhscoeff, SCIP_Real rhsoffset)

SCIP_EXPORT SCIP_RETCODE SCIPgetNlRowSOC (SCIP *scip, SCIP_CONS *cons, SCIP_NLROW **nlrow)

SCIP_EXPORT int SCIPgetNLhsVarsSOC (SCIP *scip, SCIP_CONS *cons)

SCIP_EXPORT SCIP_VAR ** SCIPgetLhsVarsSOC (SCIP *scip, SCIP_CONS *cons)

SCIP_EXPORT SCIP_RealSCIPgetLhsCoefsSOC (SCIP *scip, SCIP_CONS *cons)

SCIP_EXPORT SCIP_RealSCIPgetLhsOffsetsSOC (SCIP *scip, SCIP_CONS *cons)

SCIP_EXPORT SCIP_Real SCIPgetLhsConstantSOC (SCIP *scip, SCIP_CONS *cons)

SCIP_EXPORT SCIP_VARSCIPgetRhsVarSOC (SCIP *scip, SCIP_CONS *cons)

SCIP_EXPORT SCIP_Real SCIPgetRhsCoefSOC (SCIP *scip, SCIP_CONS *cons)

SCIP_EXPORT SCIP_Real SCIPgetRhsOffsetSOC (SCIP *scip, SCIP_CONS *cons)

SCIP_EXPORT SCIP_RETCODE SCIPaddToNlpiProblemSOC (SCIP *scip, SCIP_CONS *cons, SCIP_NLPI *nlpi, SCIP_NLPIPROBLEM *nlpiprob, SCIP_HASHMAP *scipvar2nlpivar, SCIP_Bool names)