Approximation accuracy, gradient methods, and error bound for structured convex optimization

By Paul Tseng. 2010

253 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Mathematical Physics

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Citations in the corpus

Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Łojasiewicz Condition (2016, methodology): “While the first methods that achieved this remarkable property required a memory of previous gradient values, the stochastic variance-reduced gradient (SVRG) method of Johnson and Zhang (2013) does not have this drawback. Gong and Ye (2014) show that SVRG has a linear convergence rate without SC und”
Composite objective mirror descent (2010, background): “Some notable examples include Wright et al. (2009); Nesterov (2007); Tseng (2009).”
On the Linear Convergence of a Proximal Gradient Method for a Class of Nonsmooth Convex Minimization Problems (2013, background): “The proof of Theorem 1 is rather technical and extends the analysis of Tseng [12].”
Nonparametric sparsity and regularization (2012, methodology): “The algorithm is analyzed in [9] and in [54] where it is proved that the objective values generated by such a procedure have convergence of order O(1/t2), if the step size satisfies σ ≥ L.”
A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights (2014, methodology): “− Since the introduction of Nesterov’s scheme, there has been much work on the development of ﬁrst-order accelerated methods, see Nesterov (2004, 2005, 2007) for theoretical developments, and Tseng (2008) for a uniﬁed analysis of these ideas.”
A primal–dual fixed point algorithm for convex separable minimization with applications to image restoration (2013, background): “Step 3: e Further, the authors in [1] [24, 32, 33] was also considered in [1].”
Structured Variable Selection with Sparsity-Inducing Norms (2009, methodology): “We primarily focus here on ﬁnding an efﬁcient active set algorithm; we defer to future work the design of speciﬁc SOCP solvers, e.g., based on proximal techniques (see, e.g., Tseng, 2009, and numerous references therein), adapted to such non-smooth sparsity-inducing penalties.”
A Descent Lemma Beyond Lipschitz Gradient Continuity: First-Order Methods Revisited and Applications (2017, background): “[36] P. Tseng.”
On the linear convergence of the alternating direction method of multipliers (2012, background): “The proof of Lemma 2.2 is identical to that of [35,48,53] for any ﬁxed y .”
A unified approach to error bounds for structured convex optimization problems (2015, methodology): “This answers an open question raised by Tseng [38].”
On the Linear Convergence of the Approximate Proximal Splitting Method for Non-smooth Convex Optimization (2014, background): “This result has been recently extended to the case where, f 1 ð x Þ ¼ P J 2J w J k x J k 2 and f 1 ð x Þ ¼ P J 2J w J k x J k 2 þ k k x k , where w J and k are some non-negative constants, and f 2 ¼ h ð Ax Þ is still a composite function (see [31, 36]).”
Hankel Matrix Rank Minimization with Applications to System Identification and Realization (2013, unknown): “M. FAZEL, T. K. PONG, D. SUN, AND P. TSENG 10 −3 10 −2 10 −1 10 0 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.”
Calculus of the Exponent of Kurdyka–Łojasiewicz Inequality and Its Applications to Linear Convergence of First-Order Methods (2016, methodology): “We say that the Luo-Tseng error bound 4 holds if for any ζ ≥ inf f , there exist c , (cid:15) > 0 so that It is known that this property is satisﬁed for many choices of h and P , and we refer to [28, 29, 30, 40, 41, 46] and references therein for more detailed discussions.”