Related papers: Scalable Derivative-Free Optimization Algorithms w…
We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…
This paper proposes a random subspace trust-region algorithm for general convex-constrained derivative-free optimization (DFO) problems. Similar to previous random subspace DFO methods, the convergence of our algorithm requires a certain…
Fast, gradient-based structural optimization has long been limited to a highly restricted subset of problems -- namely, density-based compliance minimization -- for which gradients can be analytically derived. For other objective functions,…
Identifying a low-dimensional informed parameter subspace offers a viable path to alleviating the dimensionality challenge in the sampled-based solution to large-scale Bayesian inverse problems. This paper introduces a novel gradient-based…
This paper presents an algorithmic framework for the minimization of strictly convex quadratic functions. The framework is flexible and generic. At every iteration the search direction is a linear combination of the negative gradient, as…
This paper proposes the method 2D-MoSub (2-dimensional model-based subspace method), which is a novel derivative-free optimization (DFO) method based on the subspace method for general unconstrained optimization and especially aims to solve…
Many canonical machine learning problems boil down to a convex optimization problem with a finite sum structure. However, whereas much progress has been made in developing faster algorithms for this setting, the inherent limitations of…
This paper considers the efficient minimization of the infinite time average of a stationary ergodic process in the space of a handful of design parameters which affect it. Problems of this class, derived from physical or numerical…
Subspace optimization methods have the attractive property of reducing large-scale optimization problems to a sequence of low-dimensional subspace optimization problems. However, existing subspace optimization frameworks adopt a fixed…
This thesis studies derivative-free optimization (DFO), particularly model-based methods and software. These methods are motivated by optimization problems for which it is impossible or prohibitively expensive to access the first-order…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
Solving large-scale optimization on-the-fly is often a difficult task for real-time computer graphics applications. To tackle this challenge, model reduction is a well-adopted technique. Despite its usefulness, model reduction often…
Superiorization reduces, not necessarily minimizes, the value of a target function while seeking constraints-compatibility. This is done by taking a solely feasibility-seeking algorithm, analyzing its perturbations resilience, and…
This paper proposes an algorithmic framework for various reconfiguration problems using zero-suppressed binary decision diagrams (ZDDs), a data structure for families of sets. In general, a reconfiguration problem checks if there is a…
Variational regularization techniques are dominant in the field of mathematical imaging. A drawback of these techniques is that they are dependent on a number of parameters which have to be set by the user. A by now common strategy to…
Derivative-free Riemannian optimization (DFRO) aims to minimize an objective function using only function evaluations, under the constraint that the decision variables lie on a Riemannian manifold. The rapid increase in problem dimensions…
This paper is devoted to the construction of order reduced method of fourth order problems. A framework is presented such that a problem on a high-regularity space can be deduced in a constructive way to an equivalent problem on three…
Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment.…
We introduce a novel framework for decentralized projection-free optimization, extending projection-free methods to a broader class of upper-linearizable functions. Our approach leverages decentralized optimization techniques with the…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…