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Line Search Methods
In this chapter we describe some of the best known line search algorithms employed in the unconstrained minimization of smooth functions. We will...
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An improvement of the Goldstein line search
This paper introduces
CLS , a new line search along an arbitrary smooth search path, that starts at the current iterate tangentially to a descent...
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A Derivative-Free Optimization Algorithm Combining Line-Search and Trust-Region Techniques
The speeding-up and slowing-down (SUSD) direction is a novel direction, which is proved to converge to the gradient descent direction under some...
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Linewalker: line search for black box derivative-free optimization and surrogate model construction
This paper describes a simple, but effective sampling method for optimizing and learning a discrete approximation (or surrogate) of a...
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A new proximal heavy ball inexact line-search algorithm
We study a novel inertial proximal-gradient method for composite optimization. The proposed method alternates between a variable metric...
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A Line Search SQP-type Method with Bi-object Strategy for Nonlinear Semidefinite Programming
We propose a line search exact penalty method with bi-object strategy for nonlinear semidefinite programming. At each iteration, we solve a linear...
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A Theoretical and Empirical Comparison of Gradient Approximations in Derivative-Free Optimization
In this paper, we analyze several methods for approximating gradients of noisy functions using only function values. These methods include finite...
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Adaptive Gradient-Free Method for Stochastic Optimization
In this paper we propose adaptive gradient-free coordinate-wise method for stochastic optimization. Adaptivity is based on line-search to...
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A Line Search Based Proximal Stochastic Gradient Algorithm with Dynamical Variance Reduction
Many optimization problems arising from machine learning applications can be cast as the minimization of the sum of two functions: the first one...
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Up to the boundary gradient estimates for viscosity solutions to nonlinear free boundary problems with unbounded measurable ingredients
In this paper, we prove up to the boundary gradient estimates for viscosity solutions to inhomogeneous nonlinear Free Boundary Problems (FBP)...
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Inexact direct-search methods for bilevel optimization problems
In this work, we introduce new direct-search schemes for the solution of bilevel optimization (BO) problems. Our methods rely on a fixed accuracy...
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A Gradient-Free Method for Multi-objective Optimization Problem
In this chapter, a gradient-free method is proposed for solving the multi-objective optimization problem in higher dimension. The concept is...
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Retraction-Based Direct Search Methods for Derivative Free Riemannian Optimization
Direct search methods represent a robust and reliable class of algorithms for solving black-box optimization problems. In this paper, the application...
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Online model adaptation in Monte Carlo tree search planning
We propose a model-based reinforcement learning method using Monte Carlo Tree Search planning. The approach assumes a black-box approximated model of...
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On polling directions for randomized direct-search approaches: application to beam angle optimization in intensity-modulated proton therapy
Deterministic direct-search methods have been successfully used to address real-world challenging optimization problems, including the beam angle...
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A class of new derivative-free gradient type methods for large-scale nonlinear systems of monotone equations
In this paper, we present a class of new derivative-free gradient type methods for large-scale nonlinear systems of monotone equations. The methods...
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Systematic Search for Singularities in 3D Euler Flows
We consider the question whether starting from a smooth initial condition 3D inviscid Euler flows on a periodic domain may develop singularities in a...
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NPROS: A Not So Pure Random Orthogonal search algorithm—A suite of random optimization algorithms driven by reinforcement learning
We live in a world where waves of novel nature-inspired metaheuristic algorithms keep hitting the shore repeatedly. This never-ending surge of new...
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Local search versus linear programming to detect monotonicity in simplicial branch and bound
This study focuses on exhaustive global optimization algorithms over a simplicial feasible set with simplicial partition sets. Bounds on the...
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Convergence of derivative-free nonmonotone Direct Search Methods for unconstrained and box-constrained mixed-integer optimization
This paper presents a class of nonmonotone Direct Search Methods that converge to stationary points of unconstrained and boxed constrained...
