22 papers · ranked by Valyu relevance
Marien Renaud, Arthur Leclaire, Nicolas Papadakis
In this document, we present the main properties satisfied by the Moreau envelope of weakly convex functions. The Moreau envelope has been introduced in convex optimization to regularize convex functionals while preserving their global minimizers. However, the Moreau envelope is also defined for the more general class…
Axel Böhm, Stephen J. Wright
We study minimization of a structured objective function, being the sum of a smooth function and a composition of a weakly convex function with a linear operator. Applications include image reconstruction problems with regularizers that introduce less bias than the standard convex regularizers. We develop a variable…
Bednarczuk, Ewa M., Bruccola, Giovanni + 4 more
In this work, we introduce a novel outer approximation scheme specifically designed for solving weakly convex constrained optimization problems. The key idea lies in utilizing quadratic cuts, rather than the traditional linear cuts, and solving an outer approximation problem at each iteration in the form of a…
Sergey Guminov, Alexander Gasnikov, Ilya Kuruzov
Convexity of the objective function often allows to guarantee much better convergence rates of iterative minimization methods than in the general non-convex case. However, many problems encountered in training neural networks are non-convex. Some of them satisfy conditions weaker than convexity, but which are still…
Valdinês Leite de Sousa Júnior, Lucas Vidal de Meireles, Samara Costa Lima, Gilson do Nascimento Silva
'Samara Costa Lima' 'Gilson do Nascimento Silva'] Abstract Since introduced by Martinet and Rockafellar, the proximal point algorithm was generalized in many fruitful directions. More recently, in 2002, Pennanen studied the proximal point algorithm without monotonicity. A year later, Iusem and Svaiter joined Pennanen…
Radu Ioan Boţ, Sorin-Mihai Grad
We propose two forward-backward proximal point type algorithms with inertial/memory effects for determining weakly efficient solutions to a vector optimization problem consisting in vector-minimizing with respect to a given closed convex pointed cone the sum of a proper cone-convex vector function with a cone-convex…
Zheming Gao, Guergana Petrova
While the classical convex optimization deals with objective functions E defined on subsets Ω in IRn for moderate values of n, see [2], some of the new applications require that the dimension n is quite large or even ∞. The design of algorithms for such cases is quite challenging since typical convergent results…
Jian Chen, Yihong Xu, Ke Zhang
In this paper, we introduce a new kind of approximate weakly efficient solutions to the set-valued vector equilibrium problems with constraints in locally convex Hausdorff topological vector spaces; then we discuss a relationship between the weakly efficient solutions and approximate weakly efficient solutions. Under…
Vladimir Temlyakov
We study sparse approximate solutions to convex optimization problems. It is known that in many engineering applications researchers are interested in an approximate solution of an optimization problem as a linear combination of elements from a given system of elements. There is an increasing interest in building such…
Hao Nguyen, Guergana Petrova
We investigate two greedy strategies for finding an approximation to the minimum of a convex function E defined on a Hilbert space H. We prove convergence rates for these algorithms under suitable conditions on the objective function E. These conditions involve the behavior of the modulus of smoothness and the modulus…
Qiao-Li Dong, Songnian He
The split equality problem (SEP) has extraordinary utility and broad applicability in many areas of applied mathematics. Recently, Byrne and Moudafi (2013) proposed a CQ algorithm for solving it. In this paper, we propose a modification for the CQ algorithm, which computes the stepsize adaptively and performs an…
Hansol X. Ryu, Manoj Srinivasan
Studying how humans perceive patterns in visually presented data is useful for understanding data-based decision-making and potentially understanding visually mediated sensorimotor control. We conducted experiments to examine how human subjects perform the simplest machine learning or statistical estimation tasks…
Abbas Kazemipour, Behtash Babadi, Min Wu, Kaspar Podgorski + 1 more
We consider the problem of optimizing general convex objective functions with nonnegativity constraints. Using the Karush-Kuhn-Tucker (KKT) conditions for the nonnegativity constraints we will derive fast multiplicative update rules for several problems of interest in signal processing, including non-negative…
Meifang Guo, Xia Li, Yongfu Su
Let H be a Hilbert space and let C be a closed convex nonempty subset of H and $T : C\rightarrow H$ a non-self nonexpansive mapping. A map $h : C\rightarrow R$ defined by $hx := \inf{\lambda \ge 0 : \lambda x+1-\lambda Tx \in C}$. Then, for a fixed $x_0 \in C$ and for $\begin{aligned}{\alpha _0}= \max…
Sylvain Prigent, Hoai-Nam Nguyen, Ludovic Leconte, Cesar Augusto Valades-Cruz + 3 more
While fluorescent microscopy imaging has become the spearhead of modern biology as it is able to generate long-term videos depicting 4D nanoscale cell behaviors, it is still limited by the optical aberrations and the photon budget available in the specimen and to some extend to photo-toxicity. A direct consequence is…
Lucian Chan, Geoffrey Hutchison, Garrett Morris
Generating low-energy molecular conformers is a key task for many areas of computational chemistry, molecular modeling and cheminformatics. Most current conformer generation methods primarily focus on generating geometrically diverse conformers rather than finding the most probable or energetically lowest minima. Here…
Lucian Chan, Geoffrey Hutchison, Garrett Morris
Generating low-energy molecular conformers is a key task for many areas of computational chemistry, molecular modeling and cheminformatics. Most current conformer generation methods primarily focus on generating geometrically diverse conformers rather than finding the most probable or energetically lowest minima. Here…
Christopher M. Wilson, Kaiqiao Li, Qiang Sun, Pei Fen Kuan + 1 more
The Cox proportional hazard model is the most widely used method in modeling time-to-event data in the health sciences. A common form of the loss function in machine learning for survival data is also mainly based on Cox partial likelihood function, due to its simplicity. However, the optimization problem becomes…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…
Peter L. Bartlett, Chris Junchi Li, Jingfeng Wu, Bin Yu
In the field of optimization, developing accelerated methods for solving minimax and fixed-point problems remains a fundamental challenge. This paper presents a novel family of dual accelerated algorithms that achieve optimal convergence rates for both minimax and fixed-point problems. By exploring new anchoring…
Michael Hutcheon, Andrew Teale
Algorithms are presented for performing a topological analysis of an arbitrary function, evaluated on an arbitrary grid of points. These algorithms work strictly by post-processing the data and require no additional function evaluations. This is achieved by connecting the grid points with a neighbourhood graph…
Authors not listed
Solving optimization problems, especially for nonlinear and constrained systems, is a challenge. Decades of specialized algorithms have been developed for general and special cases of root finding, minimization (including constraints), for parameter estimation, and mapping connected spaces. These approaches typically…