Related papers: Reduction of Linear Programming to Linear Approxim…
In this paper we introduce the notion of rational Hausdorff divisor, we analyze the dimension and irreducibility of its associated linear system of curves, and we prove that all irreducible real curves belonging to the linear system are…
Coordinate-wise minimization is a simple popular method for large-scale optimization. Unfortunately, for general (non-differentiable) convex problems it may not find global minima. We present a class of linear programs that coordinate-wise…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
In applied mathematics, especially in optimization, functions are often only provided as so called "Black-Boxes" provided by software packages, or very complex algorithms, which make automatic differentation very complicated or even…
This paper provides the first meaningful documentation and analysis of an established technique which aims to obtain an approximate solution to linear programming problems prior to applying the primal simplex method. The underlying…
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…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…
In this work, we state a general conjecture on the solvability of optimization problems via algorithms with linear convergence guarantees. We make a first step towards examining its correctness by fully characterizing the problems that are…
The simplex algorithm for linear programming is based on the fact that any local optimum with respect to the polyhedral neighborhood is also a global optimum. We show that a similar result carries over to submodular maximization. In…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
The aims of this article are two-fold. First, we give a geometric characterization of the optimal basic solutions of the general linear programming problem (no compactness assumptions) and provide a simple, self-contained proof of it…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
We propose a very simple preprocessing algorithm for semidefinite programming. Our algorithm inspects the constraints of the problem, deletes redundant rows and columns in the constraints, and reduces the size of the variable matrix. It…
Positive semidefinite programs are an important subclass of semidefinite programs in which all matrices involved in the specification of the problem are positive semidefinite and all scalars involved are non-negative. We present a parallel…
We target the problem of provably computing the equivalence between two complex expression trees. To this end, we formalize the problem of equivalence between two such programs as finding a set of semantics-preserving rewrite rules from one…
Retrograde analysis reads programs from the end to the beginning: treat statements as constraints on prior states, propagate sets of states backward, and compare the reachable inputs with the intended specification. This tutorial condenses…
A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…
A method of embedding partially ordered sets into linear spaces is presented. The problem of finding all orthocomplementations in a finite lattice is reduced to a linear programming problem.
Let $X$ be a Banach holomorphic function space on the unit disk. A linear polynomial approximation scheme for $X$ is a sequence of bounded linear operators $T_n:X\to X$ with the property that, for each $f\in X$, the functions $T_n(f)$ are…
Linear programs with quadratic regularization are attracting renewed interest due to their applications in optimal transport: unlike entropic regularization, the squared-norm penalty gives rise to sparse approximations of optimal transport…