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A tutorial on convex optimization [PDF]

Proceedings of the 2004 American Control Conference, 2004
In 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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Nonsmooth Convex Optimization

2004
(Equivalent definitions; Closed functions; Continuity of convex functions; Separation theorems; Subgradients; Computation rules; Optimality conditions.)
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Convex Optimization Via Feedbacks

SIAM Journal on Control and Optimization, 1998
Summary: Three dynamical systems are associated with a problem of convex optimization in a finite-dimensional space. For system trajectories \( x(t) \), the ratios \( x(t)/t \) are, respectively, (i) solution tracking (staying within the solution set \( X^0 \)), (ii) solution abandoning (reaching \( X^0 \) as time \( t \) goes back to the initial ...
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Generalized Convexity and Optimization

2009
The authors have written a rigorous yet elementary and self-contained book to present, in a unified framework, generalized convex functions, which are the many non-convex functions that share at least one of the valuable properties of convex functions and which are often more suitable for describing real-world problems.
CAMBINI A, MARTEIN, LAURA
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Multimodularity, Convexity and Optimization

2003
1.1 Introduction 1.1.1 Organization of the chapter 1.2 Properties of multimodular functions 1.2.1 General properties 1.2.2 Multimodularity and convexity 1.3 The optimality of bracket policies for a single criterion 1.3.1 Upper Bounds 1.3.2 Lower Bounds 1.3.3 Optimality of the Bracket Sequences
Eitan Altman, Arie Hordijk, Bruno Gaujal
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Convex optimization theory

Optimization Methods and Software, 2010
Convex optimization theory, by Dimitri P. Bertsekas, Athena Scientific, June 2009, 256 pp., $59.00 (hardcover), ISBN: 1-886529-31-0, 978-1-886529-31-1 The textbook, Convex Optimization Theory (Athe...
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Stochastic Convex Optimization

2020
In this chapter, we focus on stochastic convex optimization problems which have found wide applications in machine learning. We will first study two classic methods, i.e., stochastic mirror descent and accelerated stochastic gradient descent methods.
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Motion planning around obstacles with convex optimization

Science Robotics, 2023
Tobia Marcucci
exaly  

Concave-convex surface oxide layers over copper nanowires boost electrochemical nitrate-to-ammonia conversion

Chemical Engineering Journal, 2021
Hongjing Wang, Liang Wang, You Xu
exaly  

A Convex Optimization Toolbox

2019
This chapter presents the duality theory for optimization problems, by both the minimax and perturbation approach, in a Banach space setting. Under some stability (qualification) hypotheses, it is shown that the dual problem has a nonempty and bounded set of solutions.
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