# New sweep algorithm for solving a continuous linear-quadratic optimization problem with unseptable boundary conditions

## TL;DR

This paper introduces a new sweep algorithm for solving continuous linear-quadratic optimization problems with unseparated boundary conditions, leveraging Hamiltonian matrix symmetry to improve solution methods.

## Contribution

The paper presents a novel sweep algorithm that exploits Hamiltonian matrix symmetry to efficiently solve LQP problems with complex boundary conditions.

## Key findings

- The algorithm effectively solves LQP with unseparated boundary conditions.
- Symmetry properties of the Hamiltonian matrix simplify the solution process.
- Illustrative example demonstrates the algorithm's practical application.

## Abstract

A new algorithm for solving the solution of the linear-quadratic optimization problem (LQP) with unseparated boundary conditions in the continuous case is given. Using the properties of symmetry of the corresponding Hamiltonian matrix, the Euler-Lagrange equations, it is shown that linear algebraic equations for determining the missing initial data of the system being solved have a symmetric principal matrix. The results are illustrated by the example of LQP optimization (stationary case) with minimal control actions.

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Source: https://tomesphere.com/paper/1904.06947