Topic
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.
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TL;DR: A scalarization of vector optimization problems is proposed, where optimality is defined through convex cones and it is shown that, under mild assumptions, the dependence is differentiable for smooth objective maps defined over reflexive Banach spaces.
Abstract: A scalarization of vector optimization problems is proposed, where optimality is defined through convex cones. By varying the parameters of the scalar problem, it is possible to find all vector optima from the scalar ones. Moreover, it is shown that, under mild assumptions, the dependence is differentiable for smooth objective maps defined over reflexive Banach spaces. A sufficiency condition of optimality for a general mathematical programming problem is also given in the Appendix.
255 citations
TL;DR: This work considers the application of the conjugate gradient method to the solution of large equality constrained quadratic programs arising in nonlinear optimization, and proposes iterative refinement techniques as well as an adaptive reformulation of thequadratic problem that can greatly reduce these errors without incurring high computational overheads.
Abstract: We consider the application of the conjugate gradient method to the solution of large equality constrained quadratic programs arising in nonlinear optimization. Our approach is based implicitly on a reduced linear system and generates iterates in the null space of the constraints. Instead of computing a basis for this null space, we choose to work directly with the matrix of constraint gradients, computing projections into the null space by either a normal equations or an augmented system approach. Unfortunately, in practice such projections can result in significant rounding errors. We propose iterative refinement techniques, as well as an adaptive reformulation of the quadratic problem, that can greatly reduce these errors without incurring high computational overheads. Numerical results illustrating the efficacy of the proposed approaches are presented.
253 citations
TL;DR: A new convex nonlinear relaxation of the nonlinear GDP problem that relies on the use of the convex hull of each of the disjunctions involving nonlinear inequalities to reformulate the GDP problem as a tight MINLP problem, and for deriving a branch and bound method.
252 citations
TL;DR: In this paper, an efficient genetic algorithm (GA) is presented to solve the problem of multistage and coordinated transmission expansion planning, which is a mixed integer nonlinear programming problem, difficult for systems of medium and large size and high complexity.
Abstract: In this paper, an efficient genetic algorithm (GA) is presented to solve the problem of multistage and coordinated transmission expansion planning. This is a mixed integer nonlinear programming problem, difficult for systems of medium and large size and high complexity. The GA presented has a set of specialized genetic operators and an efficient form of generation of the initial population that finds high quality suboptimal topologies for large size and high complexity systems. In these systems, multistage and coordinated planning present a lower investment than static planning. Tests results are shown in one medium complexity system and one large size high complexity system.
251 citations
Book•
01 Dec 2000
TL;DR: In this article, a case study on design for software reliability optimization is presented, where the authors present an optimal scheduled-maintenance policy and a heuristic algorithm for optimization in reliability systems.
Abstract: List of figures List of tables Preface Acknowledgments 1 Introduction to reliability systems 2 Analysis and classification of reliability optimization models 3 Redundancy allocation by heuristic methods 4 Redundancy allocation by dynamic programming 5 Redundancy allocation by discrete optimization methods 6 Reliability optimization by nonlinear programming 7 Metaheuristic algorithms for optimization in reliability systems 8 Reliability-redundancy allocation 9 Component assignment in reliability systems 10 Reliability systems with multiple objectives 11 Other methods for system-reliability optimization 12 Burn-in optimization under limited capacity 13 Case study on design for software reliability optimization 14 Case study on an optimal scheduled-maintenance policy 15 Case studies on reliability optimization Appendices References Index
251 citations