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CoRR, 2021 This textbook is based on lectures given by the authors at MIPT (Moscow), HSE (Moscow), FEFU (Vladivostok), V.I. Vernadsky KFU (Simferopol), ASU (Republic of Adygea), and the University of Grenoble-Alpes (Grenoble, France). First of all, the authors focused on the program of a two-semester course of lectures on convex optimization, which is given to ...
Evgeniya A. Vorontsova +3 more
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Convex projection and convex multi-objective optimization [PDF]
Journal of Global Optimization, 2021 AbstractIn this paper we consider a problem, called convex projection, of projecting a convex set onto a subspace. We will show that to a convex projection one can assign a particular multi-objective convex optimization problem, such that the solution to that problem also solves the convex projection (and vice versa), which is analogous to the result ...
Gabriela Kovácová, Birgit Rudloff
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Convex Optimization of Bioprocesses
IEEE Transactions on Automatic Control, 2022 We optimize a general model of bioprocesses, which is nonconvex due to the microbial growth in the biochemical reactors. We formulate a convex relaxation and give conditions guaranteeing its exactness in both the transient and steady state cases. When the growth kinetics are modeled by the Monod function under constant biomass or the Contois function ...
Josh A. Taylor +2 more
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Convex Combinatorial Optimization [PDF]
Discrete & Computational Geometry, 2004 We introduce the convex combinatorial optimization problem, a far reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and discuss several applications.
Shmuel Onn, Uriel G. Rothblum
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Convex Optimization in Julia [PDF]
2014 First Workshop for High Performance Technical Computing in Dynamic Languages, 2014 This paper describes Convex, a convex optimization modeling framework in Julia. Convex translates problems from a user-friendly functional language into an abstract syntax tree describing the problem. This concise representation of the global structure of the problem allows Convex to infer whether the problem complies with the rules of disciplined ...
Madeleine Udell +5 more
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Predictive online convex optimization [PDF]
Automatica, 2020 We incorporate future information in the form of the estimated value of future gradients in online convex optimization. This is motivated by demand response in power systems, where forecasts about the current round, e.g., the weather or the loads' behavior, can be used to improve on predictions made with only past observations.
Antoine Lesage-Landry +2 more
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On Mixed-Integer Random Convex Programs [PDF]
, 2012 We consider a class of mixed-integer optimization problems subject to N randomly drawn convex constraints. We provide explicit bounds on the tails of the probability that the optimal solution found under these N constraints will become infeasible for the
D. Lyons +8 more
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Convex Optimization on Banach Spaces [PDF]
Foundations of Computational Mathematics, 2015 Greedy algorithms which use only function evaluations are applied to convex optimization in a general Banach space $X$. Along with algorithms that use exact evaluations, algorithms with approximate evaluations are treated. A priori upper bounds for the convergence rate of the proposed algorithms are given.
Ronald A. DeVore, Vladimir N. Temlyakov
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Convex Matroid Optimization [PDF]
SIAM Journal on Discrete Mathematics, 2003 We consider a problem of optimizing convex functionals over matroid bases. It is richly expressive and captures certain quadratic assignment and clustering problems. While generally NP-hard, we show it is polynomial time solvable when a suitable parameter is restricted.
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On convex optimization without convex representation [PDF]
Optimization Letters, 2011 7 pages; 1 ...
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