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Convex Sets and Convex Programming
1981In this chapter we concentrate on properties of convex sets in a Hilbert space and some of the related problems of importance in application to convex programming: variational problems for convex functions over convex sets, central to which are the Kuhn-Tucker theorem and the minimax theorem of von Neumann, which in turn are based on the “separation ...
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SIAM Journal on Optimization, 2010
Random convex programs (RCPs) are convex optimization problems subject to a finite number $N$ of random constraints. The optimal objective value $J^*$ of an RCP is thus a random variable. We study the probability with which $J^*$ is no longer optimal if a further random constraint is added to the problem (violation probability, $V^*$).
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Random convex programs (RCPs) are convex optimization problems subject to a finite number $N$ of random constraints. The optimal objective value $J^*$ of an RCP is thus a random variable. We study the probability with which $J^*$ is no longer optimal if a further random constraint is added to the problem (violation probability, $V^*$).
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Interior-point polynomial algorithms in convex programming
Siam studies in applied mathematics, 1994Y. Nesterov, A. Nemirovski
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Preliminaries: Convex Analysis and Convex Programming
2001In this chapter, we give some definitions and results connected with convex analysis, convex programming, and Lagrangian duality. In Part Two, these concepts and results are utilized in developing suitable optimality conditions and numerical methods for solving some convex problems.
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2001
Convex programming studies problems of the form (CP) where the objective function f: Rn → R and the constraints fi: Rn → R, i * P are “convex functions”. “Convexity” is a magic word in the world of optimization, because it allows the results for local optima to be extended to global optima.
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Convex programming studies problems of the form (CP) where the objective function f: Rn → R and the constraints fi: Rn → R, i * P are “convex functions”. “Convexity” is a magic word in the world of optimization, because it allows the results for local optima to be extended to global optima.
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Optimally linearizing the alternating direction method of multipliers for convex programming
Computational optimization and applications, 2019B. He, Fengming Ma, Xiaoming Yuan
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Motion planning around obstacles with convex optimization
Science Robotics, 2023Tobia Marcucci
exaly

