arXiv subjects

Susan Ghaderi

Publications and source records attributed to Susan Ghaderi.

7 recordsLinked to original sources

arXiv2026

Speeding Up Nonsmooth Bayesian MCMC Sampling via Inexact Proximal Unadjusted Langevin Algorithm

We study sampling from posterior distributions with nonsmooth composite potentials, a setting in which proximal-based Langevin methods are theoretically appealing but in practice limited to simple functions with closed-form proximal operators. We introduce iPULA for composite potentials, an inexact proximal unadjusted Langevin algorithm that replaces exact proximal steps with controlled approximations. Our approach leverages the Moreau envelope to smooth the potential, while allowing inexact evaluation of its gradient through inexact proximal computations. We establish non-asymptotic convergence guarantees for iPULA, explicitly characterizing the impact of inexactness on the sampling error and showing that the inexactness preserves convergence rates up to a quantifiable bias. We demonstrate the practical relevance of iPULA on a medical image reconstruction task, where proximal operators cannot be computed exactly. Experiments demonstrate the effectiveness of iPULA and support our theoretical results.

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arXiv2025

Minimizing Smooth Kurdyka-{\L}ojasiewicz Functions via Generalized Descent Methods: Convergence Rate and Complexity

This paper introduces a generalized descent algorithm (DEAL) for minimizing smooth nonconvex functions. If the objective function is nonsmooth, a smoothing technique (e.g., forward-backward and high-order Moreau envelopes) is applied to generate a smooth counterpart. The proposed framework unifies several methods, such as gradient-based methods with constant step-sizes and Armijo line search, and several proximal splitting methods. The method is built around a generalized descent inequality that adapts the amount of decrease to the geometry of the objective function. Under the Kurdyka-{\L}ojasiewicz (KL) property, we establish global convergence of the generated sequence to critical points and provide a unified convergence rate analysis. In particular, we show that the convergence behavior depends jointly on the KL exponent and the descent order, and we identify a precise condition under which generalized descent methods achieve linear convergence. By choosing the order of high-order proximal regularization according to the KL exponent, our boosted high-order proximal-point method achieves linear convergence for arbitrary KL exponents. If the objective function satisfies a global KL inequality, we further strengthen the results by proving convergence to global minimizers and deriving explicit iteration-complexity bounds. Numerical experiments validate our theoretical foundation.

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arXiv2025

(Adaptive) Scaled gradient methods beyond locally Holder smoothness: Lyapunov analysis, convergence rate and complexity

This paper addresses the unconstrained minimization of smooth convex functions whose gradients are locally Holder continuous. Building on these results, we analyze the Scaled Gradient Algorithm (SGA) under local smoothness assumptions, proving its global convergence and iteration complexity. Furthermore, under local strong convexity and the Kurdyka-Lojasiewicz (KL) inequality, we establish linear convergence rates and provide explicit complexity bounds. In particular, we show that when the gradient is locally Lipschitz continuous, SGA attains linear convergence for any KL exponent. We then introduce and analyze an adaptive variant of SGA (AdaSGA), which automatically adjusts the scaling and step-size parameters. For this method, we show global convergence, and derive local linear rates under strong convexity.

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arXiv2024

Projected subgradient methods for paraconvex optimization: Application to robust low-rank matrix recovery

This paper is devoted to the class of paraconvex functions and presents some of its fundamental properties, characterization, and examples that can be used for their recognition and optimization. Next, the convergence analysis of the projected subgradient methods with several step-sizes (i.e., constant, nonsummable, square-summable but not summable, geometrically decaying, and Scaled Polyak's step-sizes) to global minima for this class of functions is studied. In particular, the convergence rate of the proposed methods is investigated under paraconvexity and the H\"olderian error bound condition, where the latter is an extension of the classical error bound condition. The preliminary numerical experiments on several robust low-rank matrix recovery problems (i.e., robust matrix completion, image inpainting, robust nonnegative matrix factorization, robust matrix compression, and robust image deblurring) indicate promising behavior for these projected subgradient methods, validating our theoretical foundations.

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arXiv2017

Creation and analysis of biochemical constraint-based models: the COBRA Toolbox v3.0

COnstraint-Based Reconstruction and Analysis (COBRA) provides a molecular mechanistic framework for integrative analysis of experimental data and quantitative prediction of physicochemically and biochemically feasible phenotypic states. The COBRA Toolbox is a comprehensive software suite of interoperable COBRA methods. It has found widespread applications in biology, biomedicine, and biotechnology because its functions can be flexibly combined to implement tailored COBRA protocols for any biochemical network. Version 3.0 includes new methods for quality controlled reconstruction, modelling, topological analysis, strain and experimental design, network visualisation as well as network integration of chemoinformatic, metabolomic, transcriptomic, proteomic, and thermochemical data. New multi-lingual code integration also enables an expansion in COBRA application scope via high-precision, high-performance, and nonlinear numerical optimisation solvers for multi-scale, multi-cellular and reaction kinetic modelling, respectively. This protocol can be adapted for the generation and analysis of a constraint-based model in a wide variety of molecular systems biology scenarios. This protocol is an update to the COBRA Toolbox 1.0 and 2.0. The COBRA Toolbox 3.0 provides an unparalleled depth of constraint-based reconstruction and analysis methods.

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arXiv2015

Two globally convergent nonmonotone trust-region methods for unconstrained optimization

This paper addresses some trust-region methods equipped with nonmonotone strategies for solving nonlinear unconstrained optimization problems. More specifically, the importance of using nonmonotone techniques in nonlinear optimization is motivated, then two new nonmonotone terms are proposed, and their combinations into the traditional trust-region framework are studied. The global convergence to first- and second-order stationary points and local superlinear and quadratic convergence rates for both algorithms are established. Numerical experiments on the \textsf{CUTEst} test collection of unconstrained problems and some highly nonlinear test functions are reported, where a comparison among state-of-the-art nonmonotone trust-region methods show the efficiency of the proposed nonmonotne schemes.

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arXiv2014

On efficiency of nonmonotone Armijo-type line searches

Monotonicity and nonmonotonicity play a key role in studying the global convergence and the efficiency of iterative schemes employed in the field of nonlinear optimization, where globally convergent and computationally efficient schemes are explored. This paper addresses some features of descent schemes and the motivation behind nonmonotone strategies and investigates the efficiency of an Armijo-type line search equipped with some popular nonmonotone terms. More specifically, we propose two novel nonmonotone terms, combine them into Armijo's rule and establish the global convergence of sequences generated by these schemes. Furthermore, we report extensive numerical results and comparisons indicating the performance of the nonmonotone Armijo-type line searches using the most popular search directions for solving unconstrained optimization problems. Finally, we exploit the considered nonmonotone schemes to solve an important inverse problem arising in signal and image processing.

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