homotopy – Optimization Online

SQP Methods for Parametric Nonlinear Optimization

Published: 2014/02/28, Updated: 2014/07/07

Nonlinear Optimization continuation methods, homotopy, model predictive control, nonlinear constraints, nonlinear programming, parametric nonlinear programming, sequential quadratic programming, stabilized sqp

Sequential quadratic programming (SQP) methods are known to be effi- cient for solving a series of related nonlinear optimization problems because of desirable hot and warm start properties–a solution for one problem is a good estimate of the solution of the next. However, standard SQP solvers contain elements to enforce global convergence that can interfere … Read more

Lagrangian Smoothing Heuristic for Max-Cut

Published: 2002/07/15, Updated: 2002/07/16

Hernán Alperin

Ivo Nowak

Combinatorial Optimization approximation methods and heuristics, combinatorial optimization, homotopy, nonconvex optimization, pathfollowing, quadratic programming, semidefinite programming

This paper presents smoothing heuristics for an NP-hard combinatorial problem based on Lagrangian relaxation. We formulate the Lagrangian dual for this nonconvex quadratic problem and propose eigenvalue nonsmooth unconstrained optimization to solve the dual problem with bundle or subgradient methods. Derived heuristics are considered to obtain good primal solutions through pathfollowing methods using a projected … Read more