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Stochastic Convex Optimization
2020In 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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Deterministic Convex Optimization
2020In this chapter, we study algorithms for solving convex optimization problems. We will focus on algorithms that have been applied or have the potential to be applied for solving machine learning and other data analysis problems. More specifically, we will discuss first-order methods which have been proven effective for large-scale optimization.
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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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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.
openaire +2 more sources