Related papers: Generating Cutting Inequalities Successively for Q…
We present experimental and theoretical results on a method that applies a numerical solver iteratively to solve several non-negative quadratic programming problems in geometric optimization. The method gains efficiency by exploiting the…
In this paper we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints, are locally smooth. For solving this problem, we propose a…
An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…
Bilevel optimization formulates hierarchical decision-making processes that arise in many real-world applications such as in pricing, network design, and infrastructure defense planning. In this paper, we consider a class of bilevel…
Maintaining the pair similarity relationship among originally high-dimensional data into a low-dimensional binary space is a popular strategy to learn binary codes. One simiple and intutive method is to utilize two identical code matrices…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
We study an abstract setting for cutting planes for integer programming called the infinite group problem. In this abstraction, cutting planes are computed via cut generating function that act on the simplex tableau. In this function space,…
In this paper, a class of general nonlinear programming problems with inequality and equality constraints is discussed. Firstly, the original problem is transformed into an associated simpler equivalent problem with only inequality…
Two characteristics that make convex decomposition algorithms attractive are simplicity of operations and generation of parallelizable structures. In principle, these schemes require that all coordinates update at the same time, i.e., they…
Benson's outer approximation algorithm and its variants are the most frequently used methods for solving linear multiobjective optimization problems. These algorithms have two intertwined components: one-dimensional linear optimization one…
We develop a novel unified randomized block-coordinate primal-dual algorithm to solve a class of nonsmooth constrained convex optimization problems, which covers different existing variants and model settings from the literature. We prove…
Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…
In this paper, we investigate the polyhedral structure of two submodular sets with generalized upper bound (GUB) constraints, which arise as important substructures in various real-world applications. We derive a class of strong valid…
The hull of a linear code $C$ is the intersection of $C$ with its dual. To the best of our knowledge, there are very few constructions of binary linear codes with the hull dimension $\ge 2$ except for self-orthogonal codes. We propose a…
The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…
We give a survey of work on the number of vertices of the convex hull of integer points defined by the system of linear inequalities. Also, we present our improvement of some of these.
In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…
In this work, we consider two-stage quadratic optimization problems under ellipsoidal uncertainty. In the first stage, one needs to decide upon the values of a subset of optimization variables (control variables). In the second stage, the…
This paper presents the SCvx algorithm, a successive convexification algorithm designed to solve non-convex constrained optimal control problems with global convergence and superlinear convergence-rate guarantees. The proposed algorithm can…
We introduce a cutting-plane framework for nonconvex quadratic programs (QPs) that progressively tightens convex relaxations. Our approach leverages the doubly nonnegative (DNN) relaxation to compute strong lower bounds and generate…