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An important method to optimize a function on standard simplex is the active set algorithm, which requires the gradient of the function to be projected onto a hyperplane, with sign constraints on the variables that lie in the boundary of…
We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).…
We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…
In this paper we consider the problem of constructing numerical algorithms for approximating of convex compact bodies in d-dimensional Euclidean space by polytopes with any given accuracy. It is well known that optimal with respect to the…
In this work we collect and compare to each other many different numerical methods for regularized regression problem and for the problem of projection on a hyperplane. Such problems arise, for example, as a subproblem of demand matrix…
The problem of the minimization of least squares functionals with $\ell^1$ penalties is considered in an infinite dimensional Hilbert space setting. While there are several algorithms available in the finite dimensional setting there are…
Path planning plays a crucial role in various autonomy applications, and RRT* is one of the leading solutions in this field. In this paper, we propose the utilization of vertex-based networks to enhance the sampling process of RRT*, leading…
This paper studies the underlying combinatorial structure of a class of object rearrangement problems, which appear frequently in applications. The problems involve multiple, similar-geometry objects placed on a flat, horizontal surface,…
High-performance object detection relies on expensive convolutional networks to compute features, often leading to significant challenges in applications, e.g. those that require detecting objects from video streams in real time. The key to…
Recent works have developed new projection-free first-order methods based on utilizing linesearches and normal vector computations to maintain feasibility. These oracles can be cheaper than orthogonal projection or linear optimization…
This paper considers the problem of maximizing multiple linear functions over the probability simplex. A classification of feasible points is indicated. A necessary and sufficient condition for a member of each class to be an efficient…
Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order…
The Frank-Wolfe algorithm is a method for constrained optimization that relies on linear minimizations, as opposed to projections. Therefore, a motivation put forward in a large body of work on the Frank-Wolfe algorithm is the computational…
There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees,…
The multi-objective optimization is to optimize several objective functions over a common feasible set. Since the objectives usually do not share a common optimizer, people often consider (weakly) Pareto points. This paper studies…
The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…
Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating over the remaining variables. Over the last 30 years, the technique has been widely used, with empirical and…
The problem of finding a point in the intersection of closed sets can be solved by the method of alternating projections and its variants. It was shown in earlier papers that for convex sets, the strategy of using quadratic programming (QP)…
Nonlinear Parametric Optimization Network (NLPOpt-Net) is an unsupervised learning architecture to solve constrained nonlinear programs (NLP). Given the structure of an NLP, it learns the parametric solution maps with guaranteed constraint…
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…