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In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating direction type methods usually assume that the two convex functions have relatively easy…
In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
In the context of cell motility modelling and more particularly related to the Filament Based Lamelipodium Model [Manhart et al 2015 & 2017], this work deals with a rigorous mathematical proof of convergence between solutions of two…
The iteratively reweighted least squares method (IRLS) is a popular technique used in practice for solving regression problems. Various versions of this method have been proposed, but their theoretical analyses failed to capture the good…
A brief review is presented of the scaling of complex fluids, polymers and polyelectrolytes in solution and in confined geometry, in thermodynamical, structural and rheology properties using equilibrium and nonequilibrium dissipative…
In this paper we propose a class of randomized primal-dual methods to contend with large-scale saddle point problems defined by a convex-concave function $\mathcal{L}(\mathbf{x},y)\triangleq\sum_{i=1}^m f_i(x_i)+\Phi(\mathbf{x},y)-h(y)$. We…
Plasmodium stage of Physarum polycephalum behaves as a distributed dynamical pattern formation mechanism who's foraging and migration is influenced by local stimuli from a wide range of attractants and repellents. Complex protoplasmic tube…
We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a…
We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry - a variant of algebraic geometry that has attracted growing interest in applications such as computational biology, economics,…
Consider the problem of minimizing the sum of a smooth convex function and a separable nonsmooth convex function subject to linear coupling constraints. Problems of this form arise in many contemporary applications including signal…
The directed Physarum dynamics is known to solve positive linear programs: minimize $c^T x$ subject to $Ax = b$ and $x \ge 0$ for a positive cost vector $c$. The directed Physarum dynamics evolves a positive vector $x$ according to the…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
In this paper, we develop a theory of new classes of discrete convex functions, called L-extendable functions and alternating L-convex functions, defined on the product of trees. We establish basic properties for optimization: a…
We propose a novel study of the stochastic proximal gradient method for minimizing the sum of two convex functions, one of which is smooth. Under suitable assumptions and without requiring any boundedness or control of the variance of the…
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…
Robotic cloth manipulation faces challenges due to the fabric's complex dynamics and the high dimensionality of configuration spaces. Previous methods have largely focused on isolated smoothing or folding tasks and overly reliant on…
Lateral Inhibition (LI) phenomena occur in a wide range of sensory modalities and are most famously described in the human visual system. In LI the activity of a stimulated neuron is itself excited and suppresses the activity of its local…
We consider the problem of minimizing a difference of (smooth) convex functions over a compact convex feasible region $P$, i.e., $\min_{x \in P} f(x) - g(x)$, with smooth $f$ and Lipschitz continuous $g$. This computational study builds…
We study the finite element approximation of the solid isotropic material with penalization method (SIMP) for the topology optimization problem of minimizing the compliance of a linearly elastic structure. To ensure the existence of a local…