Numerical Analysis and Optimization: NAO-V, Muscat, Oman, January 2020 (Springer Proceedings in Mathematics & Statistics, 354)

Preface
A Personal Perspective on Numerical Analysis and Optimization
A Personal View of Numerical Analysis and Optimization
Contents
Contributors
A New Inexact Nonmonotone Filter Sequential Quadratic Programming Algorithm
	1 Introduction
	2 Preliminaries
	3 FiSQP Algorithm
	4 iFiSQP Algorithm
	5 Experimental Results
	6 Concluding Remarks
	References
Behavior of Limited Memory BFGS When Applied to Nonsmooth Functions and Their Nesterov Smoothings
	1 Introduction
	2 Limited Memory BFGS for Nonsmooth Optimization  in Theory
		2.1 Armijo-Wolfe Line Search
		2.2 Full BFGS
		2.3 Limited Memory BFGS
	3 Limited Memory BFGS for Nonsmooth Optimization  in Practice
		3.1 Nesterov\'s Les Houches Problem
		3.2 Smoothed Versions of Nesterov\'s Les Houches Problem
		3.3 Max Eigenvalue Problem
		3.4 Smoothed Max Eigenvalue Problem
		3.5 Semidefinite Programming
		3.6 Max Cut Problem
		3.7 Smoothed Max Cut Problem
		3.8 Matrix Completion Problem
		3.9 Smoothed Matrix Completion Problem
	4 Concluding Remarks
	References
Subgradient Smoothing Method  for Nonsmooth Nonconvex Optimization
	1 Introduction
	2 Preliminaries
	3 Theoretical Background
	4 Minimization Algorithm
		4.1 Computation of Descent Directions
		4.2 Solving Subproblem in Finding Search Directions
		4.3 Minimization Algorithms
	5 Numerical Experiments
	6 Conclusions
	References
On Some Optimization Problems  that Can Be Solved in O(n) Time
	1 Introduction
	2 Preliminaries
		2.1 Duality
		2.2 Basic Lemmas
		2.3 Simplifying Observations
		2.4 Easy and Harder Cases
	3 Analysis of the Nine Problems
		3.1 Problems of Type (1,1)
		3.2 Problems of Type (1,2)
		3.3 Problems of Type (1,infty)
		3.4 Problems of Type (2,1)
		3.5 Problems of Type (2,2)
		3.6 Problems of Type (2,infty)
		3.7 Problems of Type (infty,1)
		3.8 Problems of Type (infty,2)
		3.9 Problems of Type (infty,infty)
	4 Concluding Remarks
	References
Iteration Complexity of a Fixed-Stepsize SQP Method for Nonconvex Optimization with Convex Constraints
	1 Introduction
	2 Preliminaries
		2.1 Stationarity and Constraint Qualifications
		2.2 Giving an Explicit Bound on the Multipliers
		2.3 Detecting Stationarity
	3 Complexity Analysis
	4 Conclusions
	References
Modelling and Inferring the Triggering Function in a Self-Exciting Point Process
	1 Introduction
	2 Background
	3 Non-parametric Estimation
	4 Parametric Trigger Models
	5 Parametrised Trigger on Real Data
		5.1 EM-Algorithm
		5.2 Results on Real Data
		5.3 Prediction Results
	6 Discussion
	References
A New Multi-point Stepsize Gradient Method for Optimization
	1 Introduction
	2 MPSG Method
		2.1 Quadratic Case
		2.2 General Unconstrained Optimization
	3 Extension to Extreme Eigenvalue Problems
	4 Numerical Results
		4.1 Quadratic Optimization Problems
		4.2 Unconstrained Optimization Problems
		4.3 Extreme Eigenvalue Problems
	References
A Julia Implementation of Algorithm NCL for Constrained Optimization
	1 Introduction
	2 LANCELOT and NCL
	3 Optimal Tax Policy Problems
	4 Julia Implementation
		4.1 Key Features
		4.2 Implementation and Solver Features
		4.3 Results with Julia/NCL on the Tax Policy Problems
		4.4 Results with Julia/NCL on CUTEst Test Set
	5 Nonlinear Least Squares
	6 Summary
	7 Detailed Results for Julia/NCL on NLS Problems
	References
A Survey on Modeling Approaches  for Generation and Transmission Expansion Planning Analysis
	1 Introduction
	2 Review of GTEP Models
		2.1 Modeling Choices
		2.2 Uncertainty Inclusion
		2.3 High Level of Temporal Detail
	3 A GTEP Model for the Decarbonization of Power Systems
	4 Conclusions
	References
Second Order Adjoints in Optimization
	1 Introduction
	2 Representation of First-Order Fréchet-Derivative
	3 Representation of Second Order Fréchet-Derivative
	4 Second Order Sensitivities and Second Order Adjoints
		4.1 Sensitivity-Sensitivity Approach
		4.2 Sensitivity-Adjoint Approach
		4.3 Adjoint-Sensitivity Approach
		4.4 Adjoint-Adjoint Approach
	5 PDE-Constrained Optimization
	6 Summary and Conclusions
	References
Largest Small n-polygons: Numerical Optimum Estimates for n ≥ 6
	1 Introduction
	2 A Standard Optimization Model for Finding LSP(n)
		2.1 Model Formulation
		2.2 Numerical Challenges
	3 Related Earlier Studies
		3.1 Analytical Approaches
		3.2 Numerical Solution Approaches
		3.3 The Asymptotic Behaviour of A(n)
	4 Solving LSP Problems Numerically by AMPL-LGO
		4.1 Solution Approach
		4.2 The AMPL Model Development Environment
		4.3 LGO Solver Suite for Nonlinear Optimization
	5 Numerical Results and Comparisons
		5.1 AMPL-LGO Results
		5.2 An Illustrative Comparison with Results Obtained by Several AMPL Solvers
	6 Regression Model Development
	7 Concluding Remarks
	References
Computational Science in the 17th Century. Numerical Solution of Algebraic Equations: Digit–by–Digit Computation
	1 Introduction
	2 Stevin\'s Method 1594
	3 Viète\'s Method 1600
		3.1 Pure Equations
		3.2 Affected Equations
	4 Test Examples from Harriot 1631
	5 Test Examples from Oughtred 1647/48
	6 On Newton\'s Annotations 1664
	7 Contributions of John Wallis 1685
	8 End of an Era
	9 Computing the Square Root
	References
NAOV-2020 Conference Participants