We propose a numerical algorithm for solving smooth nonlinear programming problems with a large number of constraints, but a moderate number of variables. The active set method proceeds from a given bound mw for the maximum number of expected violated constraints, where mw is a user-provided parameter less than the total number of constraints. A … Read more
We present a new relaxation scheme for mathematical programs with equilibrium constraints (MPEC), where the complementarity constraints are replaced by a reformulation that is exact for the complementarity conditions corresponding to sufficiently non-degenerate complementarity components and relaxes only the remaining complementarity conditions. A positive parameter determines to what extent the complementarity conditions are relaxed. The … Read more
We present a primal-dual interior point method for constrained nonlinear, discrete minimax problems where the objective functions and constraints are not necessarily convex. The algorithm uses two merit functions to ensure progress towards the points satisfying the first order optimality conditions of the original problem. Convergence properties are described and numerical results provided. CitationDept. of … Read more
Identification of active constraints in constrained optimization is of interest from both practical and theoretical viewpoints, as it holds the promise of reducing an inequality-constrained problem to an equality-constrained problem, in a neighborhood of a solution. We study this issue in the more general setting of composite nonsmooth minimization, in which the objective is a … Read more
Line search algorithms for nonlinear programming must include safeguards to enjoy global convergence properties. This paper describes an exact penalization approach that extends the class of problems that can be solved with line search SQP methods. In the new algorithm, the penalty parameter is adjusted at every iteration to ensure sufficient progress in linear feasibility … Read more
In this paper, we consider the optimal design of a straight pipeline system. Suppose a gas pipeline is to be designed to transport a specified flowrate from the entry point to the gas demand point. Physical and contractual requirements at supply and delivery nodes are known as well as the costs to buy and lay … Read more
Gould and Robinson (NAR 08/18, Oxford University Computing Laboratory, 2008) gave global convergence results for a second-derivative SQP method for minimizing the exact $\ell_1$-merit function for a \emph{fixed} value of the penalty parameter. To establish this result, we used the properties of the so-called Cauchy step, which was itself computed from the so-called predictor step. … Read more
A sequential quadratic programming (SQP) method is presented that aims to overcome some of the drawbacks of contemporary SQP methods. It avoids the difficulties associated with indefinite quadratic programming subproblems by defining this subproblem to be always convex. The novel feature of the approach is the addition of an equality constrained phase that promotes fast … Read more
We present a framework for ensuring convergence of sample average approximations to stochastic optimization problems that include expectation constraints in addition to per-scenario constraints. CitationPreprint ANL/MCS 1562-1108ArticleDownload View PDF
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe an algorithmic framework based on a subproblem constructed from a linearized approximation to the objective and a regularization term. Properties of local solutions … Read more