Continuous programming part one: Linear objectives

Robust Distributed Control of Networked Systems with Linear Programming Objectives

Continuous Reformulations for Zero-one Programming Problems

In this work, we study continuous reformulations of zero–one programming problems. We prove that, under suitable conditions, the optimal solutions of a zero–one programming problem can be obtained by solving a specific continuous problem.

Continuous Optimization (Nonlinear and Linear Programming)

At the core of any optimization problem is a mathematical model of a system, which could be constructed from physical, economic, behavioral, or statistical principles. The model describes relationships between variables that define the state of the system, and may also place restrictions on the states, in the form of constraints on the variables. The model also includes an objective function, w...

A New Approach for Approximating Solution of Continuous Semi-Infinite Linear Programming

‎This paper describes a new optimization method for solving continuous semi-infinite linear problems‎. ‎With regard to the dual properties‎, ‎the problem is presented as a measure theoretical optimization problem‎, ‎in which the existence of the solution is guaranteed‎. ‎Then‎, ‎on the basis of the atomic measure properties‎, ‎a computation method was presented for obtaining the near optimal so...

One-bit compressed sensing by linear programming

We give the first computationally tractable and almost optimal solution to the problem of one-bit compressed sensing, showing how to accurately recover an s-sparse vector x ∈ R from the signs of O(s log(n/s)) random linear measurements of x. The recovery is achieved by a simple linear program. This result extends to approximately sparse vectors x. Our result is universal in the sense that with ...