Conic Programming in GAMS
Description
Conic programming models minimize a linear function over
the intersection of an affine set and the product of nonlinear cones. The
problem class involving second order (quadratic) cones is known as Second
Order Cone Programs (SOCP). These are nonlinear convex problems that
include linear and (convex) quadratic programs as special cases.
Conic programs allow the formulation of a wide variety of application
models, including problems in
-
Portfolio Optimization
-
Truss Topology Design in Structural Engineering
-
FIR Filter Design and Signal Processing
-
Antenna Array Weight Design
-
Quadratic Programming
-
Robust linear programming
-
Norm Minimization Problems
For more information see
and the references below.
Sample Conic Models in GAMS:
- emfl_socp.gms:
Multiple facility location problem.
- fir_socp.gms:
Linear phase lowpass filter design model
- qp7.gms:
Portfolio investment model using rotated quadratic cones
(quadratic program using a Markowitz model)
- springs.gms:
Equilibrium of system with piecewise linear springs
- trussm.gms:
Truss topology design problem with multiple loads
References and Links
-
Aharon Ben-Tal and Arkadi Nemirovski, Lectures
on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications,
MPS/SIAM Series on Optimization, SIAM Press, 2001.
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M. Lobo, L. Vandenberghe, S. Boyd, and H. Lebret , Applications
of second-order cone programming, Linear Algebra and its Applications,
284:193-228, November 1998, Special Issue on Linear Algebra in Control,
Signals and Image Processing.
-
Pataki, G, and Schmieta, S, The DIMACS library of
semidefinite-quadratic-linear programs. Tech. rep., Computational
Optimization Research Center, Columbia University, 2002.
-
Seventh
Dimacs Implementation Challenge
on Semidefinite and Related Optimization Problems.
