Nonlinear programming

About: Nonlinear programming is a research topic. Over the lifetime, 19486 publications have been published within this topic receiving 656602 citations. The topic is also known as: non-linear programming & NLP.

Superlinear Convergence of a Stabilized SQP Method to a Degenerate Solution

Abstract: We describe a slight modification of the well-known sequential quadratic programming method for nonlinear programming that attains superlinear convergence to a primal-dual solution even when the Jacobian of the active constraints is rank deficient at the solution We show that rapid convergence occurs even in the presence of the roundoff errors that are introduced when the algorithm is implemented in floating-point arithmetic

An Algorithm for Solving the General Bilevel Programming Problem

Abstract: The conflict that naturally arises in a hierarchical system can often be modeled as a multistage optimization problem. This paper considers the sequential uncooperative problem in which two decision makers wish to maximize their own objective functions over a feasible region defined by interactive strategy sets. The resultant problem is known as the bilevel program. Such programs are inherently nonconvex and resistant to standard nonlinear programming solution techniques such as piecewise linearization and convex underestimating envelopes. Alternatively, a grid search algorithm is offered which exhibits the desirable property of monotonicity. The algorithm is based on two sets of necessary conditions previously developed and combined here to provide an operational check for stationarity and local optimality. Potential solutions are obtained from a parameterized master program whose feasible region approximates that of the original problem. As the one-dimensional parameter is varied over the unit interval ...

Sensitivity analysis of nonlinear programs and differentiability properties of metric projections

Abstract: This paper is concerned with a study of differentiability properties of the optimal value function and an associated optimal solution of a parametrized nonlinear program. Second order analysis is presented essentially under the Mangasarian-Fromovitz constraint qualification when the corresponding vector of Lagrange multipliers is not necessarily unique. It is shown that under certain regularity conditions the optimal value function possesses second order directional derivatives and the optimal solution mapping is directionally differentiable. The results obtained are applied to an investigation of metric projections in finite-dimensional spaces.