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## Equilibrium of system of piecewise linear springs

This problem describes a mechanical system to find a hanging chain consisting of links. The first and last nodes are fixed. Each node has a weight hanging from it. The problem is to minimize the energy of the system (see [5,15]):

 (3-10)

where is the acceleration due to gravity, is the stiffness constant of the springs, is the rest length of each spring, and is an upper bound on the spring energy of the -th spring. Consider , , , , , , . Then and . The objective function becomes Furthermore,

The linear and cone constraints are

Example 6. The data is the same as in springs.mod in [16]. We have and . We use as test cases.

Hans D. Mittelmann 2003-09-10