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An algorithm for unconstrained optimization
International Journal of Computer Mathematics, 1992In this note an algorithm for solving unconstrained optimization problems is presented. A convergence analysis for the method is considered too. The rate of convergence is shown to be superlinear. Numerical results are reported.
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A View of Unconstrained Optimization.
1987Abstract : Finding the unconstrained minimizer of a function of more than one variable is an important problem with many practical applications, including data fitting, engineering design, and process control. In addition, techniques for solving unconstrained optimization problems form the basis for most methods for solving constrained optimization ...
null Robert B. +2 more
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Unconstrained Optimization Problems
2010Unconstrained optimization methods seek a local minimum (or a local maximum) in the absence of restrictions, that is, $$f(x) \longrightarrow \min (x \in D)$$ for a real-valued function f: D → ℝ defined on a nonempty subset D of ℝ n for a given n ∈ ℕ.
Dieter Hoffmann, Wilhelm Forst
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Equations and Unconstrained Optimization
2014In this chapter, we start our discussion of Newton-type methods, which are based on the fundamental principle of linear/quadratic approximation of the problem data (or of some part of the problem data). The underlying idea is extremely important, as it serves as a foundation for numerous computationally efficient algorithms for optimization and ...
Mikhail V. Solodov, Alexey F. Izmailov
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Unconstrained Optimization Algorithms
2019In this chapter, we will present the most representative algorithms for solving an optimization problem without functional constraints, that is, the problem $$ \begin{array}{lll} P: &{} \text {Min} &{} f(x) \\ &{} \text {s.t.} &{} x\in C, \end{array} $$ where \(\emptyset \ne C\subset \mathop {\mathrm {dom}}f\subset \mathbb {R}^{n}.\) We will ...
Francisco J. Aragón +3 more
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An incremental decomposition method for unconstrained optimization
Applied Mathematics and Computation, 2014In this work we consider the problem of minimizing a sum of continuously differentiable functions. The vector of variables is partitioned into two blocks, and we assume that the objective function is convex with respect to a block-component. Problems with this structure arise, for instance, in machine learning.
BRAVI, LUCA, SCIANDRONE, MARCO
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Basics of Unconstrained Optimization
2019The objectives of this chapter are to: Discuss different techniques for solving unconstrained optimization problems of a single variable Study the necessary and sufficient conditions for optimizing a function of several variables.
Asoke Kumar Bhunia +2 more
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An Overview of Unconstrained Optimization
1994Developments in the theory and practice of unconstrained optimization are described. Both line search and trust region prototypes are explained and various algorithms based on the use of a quadratic model are outlined. The properties and implementation of the BFGS method are described in some detail and the current preference for this approach is ...
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Few Topics in Unconstrained Optimization
2021Unconstrained optimization is, on the one hand, a classical topic in optimization, which goes back to the seventeenth century. On the other hand, it is a modern one, which undergone substantial transformation in the last few decades.
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Criteria for Unconstrained Global Optimization
Journal of Optimization Theory and Applications, 2007We develop criteria for the existence and uniqueness of the global minima of a continuous bounded function on a noncompact set. Special attention is given to the problem of parameter estimation via minimization of the sum of squares in nonlinear regression and maximum likelihood.
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