http://galton.uchicago.edu/~lekheng/courses/310w11/boyd-socp.pdf

Applications of second-order cone programming

A new methodology for constructing convex optimization models called disciplined convex programming is introduced. The methodology enforces a set of conventions upon the models constructed, in turn allowing much of the work required to analyze and solve the models to be automated.

/pdf/disciplined-convex-programming-46i3cp8qhe.pdf

Disciplined Convex Programming

conditions and an accurate semidefinite programming solver," The Journal of the SDPA family for solving large-scale SDPs," in Handbook on Semidefinite. Semidefinite Programming, Combinatorial. Optimization and Primal semidefinite programming problem Handbook of Semidefinite Programming. Kluwer. Solving Euclidean distance matrix completion problems via semidefinite programming. AY Alfakih, A Khandani, H Wolkowicz. Computational optimization.

/pdf/handbook-of-semidefinite-programming-1hywp52iad.pdf

Handbook of Semidefinite Programming

We present and motivate a new model of the truss topology design problem, where the rigidity of the resulting truss with respect both to given loading scenarios and small "occasional" loads is optimized It is shown that the resulting optimization problem is a semidefinite program We derive and analyze several equivalent reformulations of the problem and present illustrative numerical examples

https://www2.isye.gatech.edu/~nemirovs/SIOPT_RTTD_1997.pdf

Robust Truss Topology Design via Semidefinite Programming

Truss topology design for minimum external work (compliance) can be expressed in a number of equivalent potential or complementary energy problem formulations in terms of member forces, displacements and bar areas. Using duality principles and non-smooth analysis we show how displacements only as well as stresses only formulations can be obtained and discuss the implications these formulations have for the construction and implementation of efficient algorithms for large-scale truss topology design. The analysis covers min-max and weighted average multiple load designs with external as well as self-weight loads and extends to the topology design of reinforcement and the topology design of variable thickness sheets and sandwich plates. On the basis of topology design as an inner problem in a hierarchical procedure, the combined geometry and topology design of truss structures is also considered. Numerical results and illustrative examples are presented.

Optimization Methods for Truss Geometry and Topology Design

Maximum strength elastic truss structural design is conveniently formulated in terms of displacements and bar volumes. The resulting problem is nonconvex, and for topology design very large, as one seeks the optimal topology as a subset of a large number of potential bars connecting all nodal points of an initially chosen set. In this paper we present a number of equivalent formulations in the displacements only, taking full advantage of the structure of the optimization problem. The equivalent formulations are of min-max type or are quadratic programming problems in the displacements, reducing in some cases even to linear programming problems.

Equivalent displacement based formulations for maximum strength Truss topology design

We consider a simple model of damage, where damage is interpreted as the removal of material from a given truss structure. Occuring damage in a given scenario is modelled by a damage contribution which maximizes compliance. Assuming linear elasticity this leads to an optimization problem formulated in displacements and a set of variables which describe the damaged material of each bar in the truss. A sequence of such problems models damage as a time-dependent process, i.e. damage evolution is considered. A simple ad-hoc-method for the resulting nonconvex problems can be interpreted as a descent algorithm of feasible directions which reaches a local optimum in a finite number of steps. Some numerical examples show the use of the algorithm.

W. Achtziger

Papers

Equivalent displacement based formulations for maximum strength Truss topology design

Design for maximal flexibility as a simple computational model of damage