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.

Optimal scheduling of rehabilitation activities for multiple pavement facilities: exact and approximate solutions

Abstract: This paper presents a mathematical programming model for optimal highway pavement rehabilitation planning which minimizes the life-cycle cost for a finite horizon. It extends previous researches in this area by solving the problem of multiple rehabilitation activities on multiple facilities, with realistic empirical models of deterioration and rehabilitation effectiveness. The formulation is based on discrete control theory. A nonlinear pavement performance model and integer decision variables are incorporated into a mixed-integer nonlinear programming (MINLP). Two solution approaches, a branch-and-bound algorithm and a greedy heuristic, are proposed for this model. It is shown that the heuristic results provide a good approximation to the exact optima, but with much lower computational costs.

The TOMLAB Optimization Environment

Abstract: The TOMLAB Optimization Environment is a powerful optimization tool in MATLAB, which incooperates many results from the last 40 years of research in the field. More than 70 different algorithms for linear, discrete, global and nonlinear optimization are implemented in TOMLAB, and a large number of C and Fortran solvers are also fully integrated. The environment is call-compatible with Math-Works’ Optimization Toolbox, and supports problems formulated in AMPL. This chapter discusses the design and contents of TOMLAB, and examplifies its usage on a practical optimization problem. The objective is to present the overall design and describe how to efficiently model a problem in TOMLAB using the standard structures and assign statements. More information about TOMLAB is available at URL: http: //tomlab. BIZ.

Numerical methods for large-scale nonlinear optimization

Abstract: Recent developments in numerical methods for solving large differentiable nonlinear optimization problems are reviewed. State-of-the-art algorithms for solving unconstrained, bound-constrained, linearly constrained and non-linearly constrained problems are discussed. As well as important conceptual advances and theoretical aspects, emphasis is also placed on more practical issues, such as software availability.

Second-order and related extremality conditions in nonlinear programming

Abstract: This paper is concerned with the problem of characterizing a local minimum of a mathematical programming problem with equality and inequality constraints. The main object is to derive second-order conditions, involving the Hessians of the functions, or related results where some other curvature information is used. The necessary conditions are of the Fritz John type and do not require a constraint qualification. Both the necessary conditions and the sufficient conditions are given in equivalent pairs of primal and dual formulations.

Reliability-based optimization of structural systems

Abstract: A method to carry out a Reliability-Based Optimization (RBO) of especially nonlinear structural systems is introduced. Statistical uncertainties involving both structural and loading properties are considered. The concept is based on the separation of structural reliability analyses and the optimization procedures. Two approaches are discussed, depending on the interaction of reliability analysis and mathematical programming and the way of representation of the limit state functions (LSF) of the structure. As, for cases of practical significance, the LSF is known only pointwise it is approximated by Response Surfaces (RS). For the response calculations Finite Element (FE) procedures are utilized. Failure probabilities are determined by applying variance reducing Monte Carlo simulation (MCS) techniques such as Importance Sampling (IS). Following the reliability analysis, the optimization procedure is controlled by the NLPQL algorithm. A numerical example in terms of a template ocean platform exemplifies the procedures.