In this talk we motivate further research in signomial programming (SP) for the solution of conceptual engineering design problems. We use examples from aerospace engineering, from aircraft design to network design and control, to demonstrate the modeling capabilities and solution quality of SPs, and identify areas for future work. We introduce GPkit, a toolkit that provides abstractions, modeling tools and solution methods to use SPs to explore complex tradespaces. Additionally, we present methods to solve SPs under uncertainty, called robust SPs, to trade off risk and performance.
joint work with Venkat Chandrasekaran, Adam Wierman
We show how SAGE nonnegativity certificates are compatible with a technique known as partial dualization, whereby computationally tractable constraints are incorporated into a dual problem without being moved to the Lagrangian. We consider the resulting "generalized SAGE cone" as it pertains to signomial programming (SP). Matters such as coordinate system invariance, sparsity preservation, and error bounds are addressed. Our provided implementation shows that this approach can solve many SPs from the literature to global optimality, without resorting to cutting planes, or branch-and-bound.
joint work with Steven Diamond, Stephen Boyd
We introduce log-log convex programs (LLCPs): optimization problems with positive variables that become convex when the variables, objective functions, and constraint functions are replaced with their logs. LLCPs strictly generalize geometric programming, and include interesting problems involving nonnegative matrices, and integral inequalities. We discuss the basic calculus for this class of functions, and show when a given LLCP can be cast to a format that is acceptable by modern conic solvers. Illustrative examples are provided with CVXPY's new "disciplined geometric programming" feature.