Approximate Methods In Optimization Problems

By S. Decker. 2016

101 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Optimization

Citations in the corpus

Affine Invariant Analysis of Frank-Wolfe on Strongly Convex Sets (2020, methodology): “…-ball, deﬁned as Speciﬁcally, we compare our aﬃne invariant backtracking method in Algorithm 2 against the naive FW Algorithm 1 with step size 1 /L [Demyanov et al. 1970] and L L The reason why adaptive FW methods are slower in the left ﬁgure is because, in the worst case, the number of iterations…”
Frank-Wolfe Algorithms for Saddle Point Problems (2016, methodology): “The Frank-Wolfe (FW) optimization algorithm (Frank and Wolfe, 1956), also known as the conditional gradient method (Demyanov and Rubinov, 1970), is a ﬁrst-order method for smooth constrained optimization over a compact set.”
Curvature of Feasible Sets in Offline and Online Optimization (2020, background): “There has been much interest in the influence of curvature on computational and statistical efficiency in optimization and machine learning, with the use of notions of curvature such as strong convexity and gauge bodies in convex optimization [1, 12, 13, 18, 32], and uniform convexity/martingale-cot”
Frank-Wolfe Method is Automatically Adaptive to Error Bound Condition (2018, background): “Many previous works (e.g., (Levitin and Polyak, 1966; Demyanov and Rubinov, 1970; Dunn, 1979; Garber and Hazan, 2015)) considered this condition of feasible set when studying the FW method.”
Solving variational inequalities with monotone operators on domains given by Linear Minimization Oracles (2013, background): “…in this line of research is on smooth/smooth norm-regularized convex minimization [11,13,14,16,17,31], where the main “working horse” is the classical Conditional Gradient (a.k.a. Frank-Wolfe) algorithm originating from [12] and intensively studied in 1970’s (see [9,10,28] and references therein).”
New analysis and results for the Frank–Wolfe method (2013, methodology): “As early as 1970, Demyanov and Rubinov [3] used the FW gap quantities extensively in their convergence proofs of the Frank-Wolfe method, and perhaps this quantity was used even earlier.”
On lower complexity bounds for large-scale smooth convex optimization (2013, methodology): “d instances for nonsmooth convex minimization [1], which now are properly smoothed by the inf-convolution. 1Originating from [4], Conditional Gradient algorithm was intensively studied in 1970’s (see [5, 6] and references therein); recently, there is a signiﬁcant burst of interest in this technique,”
Linear Bandits on Uniformly Convex Sets (2021, unknown): “Such observations have already been made, e.g. , in constrained optimization [Pol66; DR70; Dun79; KdP21b; Ker+20], when the sets’ α -strong convexity leads to linear convergence rates of the Frank-Wolfe methods with a conditioning on the set that does not depend on the dimension.”
Revisiting Projection-Free Optimization for Strongly Convex Constraint Sets (2018, background): “Prior work (Levitin and Polyak 1966; Demyanov and Rubinov 1970; Dunn 1979) shows that standard FW without line search for smooth functions can achieve an exponential convergence rate, by making a strict assumption that the gradient is lower-bounded everywhere in the feasible set.”
Projection-Free Optimization on Uniformly Convex Sets (2020, methodology): “…analyses of the simple Follow-The-Leader (FTL) for online linear optimization (Huang et al., 2016) is analogous to the oﬄine convergence analyses of the Frank-Wolfe algorithm when not assuming strong-convexity of the objective function as in (Polyak, 1966; Demyanov and Rubinov, 1970; Dunn, 1979).”