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.

Proximal Subgradients, Marginal Values, and Augmented Lagrangians in Nonconvex Optimization

Abstract: The Clarke subgradients of a nonconvex function p on Rn are characterized in terms of limits of “proximal subgradients.” In the case where p is the optimal value function in a nonlinear programming problem depending on parameters, proximal subgradients correspond to saddlepoints of the augmented Lagrangian. When the constraint and objective functions are sufficiently smooth, this leads to a characterization of marginal values for a given problem in terms of limits of Lagrange multipliers in “neighboring” problems for which the standard second-order sufficient conditions for optimality are satisfied at a unique point.

Global optimization for sustainable design and synthesis of algae processing network for CO2 mitigation and biofuel production using life cycle optimization

Abstract: Global optimization for sustainable design and synthesis of a large-scale algae processing network under economic and environmental criteria is addressed. An algae processing network superstructure including 7800 processing routes is proposed. Based on the superstructure, a multiobjective mixed-integer nonlinear programming (MINLP) model is developed to simultaneously optimize the unit cost and the unit global warming potential (GWP). To efficiently solve the nonconvex MINLP model with separable concave terms and mixed-integer fractional terms in the objective functions, a global optimization strategy that integrates a branch-and-refine algorithm based on successive piecewise linear approximations is proposed and an exact parametric algorithm based on Newton’s method. Two Pareto-optimal curves are obtained for biofuel production and biological carbon sequestration, respectively. The unit annual biofuel production cost ranges from $7.02/gasoline gallon equivalent (GGE) to $9.71/GGE, corresponding to unit GWP’s of 26.491 to 16.52 kg CO2-eq/GGE, respectively. V C 2014 American Institute of Chemical Engineers AIChE J, 60: 3195–3210, 2014

Manopt, a Matlab toolbox for optimization on manifolds

Abstract: Optimization on manifolds is a rapidly developing branch of nonlinear optimization. Its focus is on problems where the smooth geometry of the search space can be leveraged to design efficient numerical algorithms. In particular, optimization on manifolds is well-suited to deal with rank and orthogonality constraints. Such structured constraints appear pervasively in machine learning applications, including low-rank matrix completion, sensor network localization, camera network registration, independent component analysis, metric learning, dimensionality reduction and so on. The Manopt toolbox, available at this http URL, is a user-friendly, documented piece of software dedicated to simplify experimenting with state of the art Riemannian optimization algorithms. We aim particularly at reaching practitioners outside our field.

Optimization strategies for the vulnerability analysis of the electric power grid.

Abstract: Identifying small groups of lines, whose removal would cause a severe blackout, is critical for the secure operation of the electric power grid. We show how power grid vulnerability analysis can be studied as a mixed integer nonlinear programming (minlp) problem. Our analysis reveals a special structure in the formulation that can be exploited to avoid nonlinearity and approximate the original problem as a pure combinatorial problem. The key new observation behind our analysis is the correspondence between the Jacobian matrix (a representation of the feasibility boundary of the equations that describe the flow of power in the network) and the Laplacian matrix in spectral graph theory (a representation of the graph of the power grid). The reduced combinatorial problem is known as the network inhibition problem, for which we present a mixed integer linear programming formulation. Our experiments on benchmark power grids show that the reduced combinatorial model provides an accurate approximation, to enable vulnerability analyses of real-sized problems with more than 10,000 power lines.