Lectures on modern convex optimization

By Arkadi Nemirovski. 1987

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Citations in the corpus

Byzantine Stochastic Gradient Descent (2018, background): “We remark that • The first term O ( GD √ T ) is the classical error rate for gradient descent on non-smooth objectives [5], and should exist even if V = 0 (so every ∇k,i exactly equals ∇f(xk)) and α = 0.”
Isotonic Smoothing Spline Regression (2008, methodology): “The SOCP was studied by many authors (e.g. Lobo, Vandenberghe, Boyd, and Lebert 1998; Ben-Tal and Nemirovski 2001) in applied mathematics and operation research areas.”
Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent (2014, unknown): “For a more detailed survey, we recommend the textbooks [9, 26].”
Accelerated Mirror Descent in Continuous and Discrete Time (2015, methodology): “The mirror descent method also provides an important generalization of the gradient descent method to non-Euclidean geometries, as discussed in [19, 3], and has many applications in convex optimization [6, 5, 12, 15], as well as online learning [9, 11].”
A sequential parametric convex approximation method with applications to nonconvex truss topology design problems (2010, background): “The latter fact is proved in [4], here we give a shorter self contained proof.”
Much Faster Algorithms for Matrix Scaling (2017, background): “(24)This proof can be found for instance in the textbook [6].”
On Complexity of Stochastic Programming Problems (2005, methodology): “This is the approach of robust optimization (cf., Ben-Tal and Nemirovski [6]).”
PENNON: A code for convex nonlinear and semidefinite programming (2003, methodology): “Normally formulated as LP, here reformulated as SDP for testing purposes (see, eg, [2, 11]).”
An introduction to continuous optimization for imaging (2016, background): “The extensive monograph by Ben-Tal and Nemirovski (2001)9 presents many possible variants, with rates.”
Robust sample average approximation (2014, background): “Optimization over canonical cones is tractable both theoretically and practically using state-of-the-art interior point algorithms [4].”
Performance of first-order methods for smooth convex minimization: a novel approach (2012, background): “The promised numerical bound now easily follows showing that a complexity bound for (FO) is determined by the optimal value of the dual problem (DQ ′ ) which can be computed eﬃciently by any numerical algorithm for SDP (see e.g., [6, 10, 19]).”
User-Centric 5G Cellular Networks: Resource Allocation and Comparison With the Cell-Free Massive MIMO Approach (2018, background): “2Although polynomial, the best known upper-bound for the complexity of generic convex problems scales with the fourth power of the number of variables, while many classes of convex problems admit a cubic complexity [21].”
Strong Duality in Conic Linear Programming: Facial Reduction and Extended Duals (2013, background): “Assuming that K is nice, in Section 4 we arrive at the representation in (1.1), i.e., show that F ∗min is the projection of a conic linear system, and derive an extended dual for conic LPs over nice cones.”
Living on the edge: phase transitions in convex programs with random data (2013, background): “ams. When C ˘S n£ ¯ , we recover the class of (real) semideﬁnite programs. In addition to their ﬂexibility and modeling power, cone programs enjoy effective algorithms and a crisp theory. We refer to [BTN01] for further details. The cone program (8.1) can exhibit several interesting behaviors. Let u”
Parameter Estimation in Stochastic Differential Equations (2011, methodology): “By this, a bridge has been offered between statistical learning and data mining on the one hand, and the powerful tools prepared for well-structured convex optimization problems [7,27], and Newton- and steepest-descent type regression methods [2, 26] on the other hand.”