A perturbation view of level-set methods for convex optimization

Level-set methods for convex optimization

Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the roles of the objective and constraint functions, and instead approximately solves a sequence of parametric level-set problems. A zero-finding procedure, base...

A Mathematical View of Interior Point Methods for Convex Optimization

A Level-set Method for Convex Optimization with A

Large-scale constrained convex optimization problems arise in several application 4 domains. First-order methods are good candidates to tackle such problems due to their low iteration 5 complexity and memory requirement. The level-set framework extends the applicability of first-order 6 methods to tackle problems with complicated convex objectives and constraint sets. Current methods 7 based on...

A BINARY LEVEL SET METHOD FOR STRUCTURAL TOPOLOGY OPTIMIZATION

This paper proposes an effective algorithm based on the level set method (LSM) to solve shape and topology optimization problems. Since the conventional LSM has several limitations, a binary level set method (BLSM) is used instead. In the BLSM, the level set function can only take 1 and -1 values at convergence. Thus, it is related to phase-field methods. We don’t need to solve the Hamilton-Jac...

Cutting-set methods for robust convex optimization with pessimizing oracles

We consider a general worst-case robust convex optimization problem, with arbitrary dependence on the uncertain parameters, which are assumed to lie in some given set of possible values.We describe a general method for solving such a problem, which alternates between optimization and worst-case analysis. With exact worst-case analysis, the method is shown to converge to a robust optimal point. ...