The minimum principle in the optimization of bar systems The theoretical basis of optimal control methods The formal structure of an optimal control problem Necessary optimality conditions The basic optimal control task The nonautonomous task in optimal control Optimal control tasks with various types of constraints Multi-interval tasks with discontinuities in state variables Numerical methods of optimization Indirect methods Direct methods Numerical software Optimization of bar systems in the minimum principle formal structure Objective function Control variables State equations Boundary conditions and interior point conditions Constraint conditions Examples of the optimal shaping of solid bar axes An optimization task with reference to the minimization of maximum normal stress with a single control variable Optimization task structure Necessary optimality conditions Numerical results. A task without axis trajectory constraints Numerical results. A task with axis trajectory constraints An optimization task with reference to the minimization of maximum normal stress with many control variables Conclusions and summary of the optimization tasks with reference to minimization of maximum normal stress An optimization task with reference to volume minimization. Bar systems with a rational axis Optimal solution and numerical results for tasks with a single control variable Numerical results for a task with two control variables The task of optimal shaping of a solid bar with reference to stability Searching for critical load values Optimal shaping of an arch with reference to critical load maximization Examples of the optimal shaping of thin-walled bars The problem of optimal solutions in practical terms Characteristics of the optimized thin-walled bar Optimization task structure Numerical results. Linear solutions The problem of a piecewise constant solution A bar optimization task considering implicit boundary conditions