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RAIRO - Operations Research, 2019
Many optimization problems are formulated from a real scenario involving incomplete information due to uncertainty in reality. The uncertainties can be expressed with appropriate probability distributions or fuzzy numbers with a membership function, if enough information can be accessed for the construction of either the probability density function or
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Many optimization problems are formulated from a real scenario involving incomplete information due to uncertainty in reality. The uncertainties can be expressed with appropriate probability distributions or fuzzy numbers with a membership function, if enough information can be accessed for the construction of either the probability density function or
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A tutorial on convex optimization
Proceedings of the 2004 American Control Conference, 2004In recent years, convex optimization has become a computational tool of central importance in engineering, thanks to it's ability to solve very large, practical engineering problems reliably and efficiently. The goal of this tutorial is to give an overview of the basic concepts of convex sets, functions and convex optimization problems, so that the ...
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Depth-Optimized Convexity Cuts
Annals of Operations Research, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jonathan Eckstein, Mikhail Nediak
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Lower bounds for non-convex stochastic optimization
Mathematical programming, 2019We lower bound the complexity of finding $$\epsilon $$ ϵ -stationary points (with gradient norm at most $$\epsilon $$ ϵ ) using stochastic first-order methods.
Yossi Arjevani +5 more
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Convex Optimization With Convex Constraints
2001In this chapter we want to solve the problem minf(x) | x ∈ C, where f is a convex function on ℝ n , and C is a convex, nonempty subset of ℝ n . A point x* ∈ C is a global solution, or more simply a solution to this problem, or a minimizer of f on C, if f(x*) ≤ f(x), ∀x ∈ C. We say that x* is a local solution to this problem if there exists a relatively
Monique Florenzano, Cuong Le Van
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Optimal Rocket Landing Guidance Using Convex Optimization and Model Predictive Control
Journal of Guidance Control and Dynamics, 2019In this paper, a novel guidance algorithm based on convex optimization, pseudospectral discretization, and a model predictive control (MPC) framework is proposed to solve the highly nonlinear and c...
Jinbo Wang, Naigang Cui, Changzhu Wei
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Optimization on directionally convex sets
Central European Journal of Operations Research, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On A characterization of optimality in convex programming
Mathematical Programming, 1976Necessary and sufficient conditions for optimality are given, for convex programming problems, without constraint qualification, in terms of a single mathematical program, which can be chosen to be bilinear.
Adi Ben-Israel, Aharon Ben-Tal
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Nesterov's Method for Convex Optimization
SIAM Review, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Duality in Reverse Convex Optimization
SIAM Journal on Optimization, 1998Summary: A duality theorem for the general problem of minimizing an extended real-valued convex function on a locally convex linear space under a reverse convex constraint is considered. In the particular case of the distance to a reverse convex subset in a normed linear space, we recover as a corollary a duality theorem due to \textit{C.
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