Convex Cost Function Research Articles

Nonconvex Structural Optimization Problems

Plastic optimization problems involving convex specific cost functions can be handled by several methods. The earliest technique was based on the uniform energy dissipation principle; a more general approach which could be termed the cost gradiend method was developed later and was extended to multiload, multicomponent systems and to preassigned strength distribution. Some used energy principles in deriving their methods while others used a direct variational method involving slack variables and Lagrangian multipliers. All the foregoing criteria were developed originally as sufficient conditions for various classes of convex cost functions. If the cost function is nonconvex, then the kinematic conditions given by either variational method or by the Prager-Shield approach can be shown to constitute only a necessary condition for a local minimum. In deriving optimal solutions for frames and shells associated with nonconvex cost functions, it has been found that these criteria can still be very useful because they often admit only one (unique) solution. A simple example is presented which demonstrates this method.

A Unified Formulation of the Theory of Optimal Plastic Design with Convex Cost Function

A Unified Formulation of the Theory of Optimal Plastic Design with Convex Cost Function

Duality between Limit Analysis and Limit Design

The relation between limit analysis and optimal limit design of stable rigid perfectly plastic systems will be analyzed in the particular context of Tresca sandwich plates, but the same duality principles can be readily extended to any yield condition and any convex and piece-wise differentiable specific cost function.

Numerical computation of optimal control sequences and trajectories

An iterative technique for solving state and control-constrained linear optimal control problems with strictly convex cost functions is described. The computational procedure makes use of a previously developed gradient method which is generalized by the inclusion of new kinds of constraints and modified by the consideration of projections onto specified sets.

An iterative procedure for solving convex optimal control problems

A doubly iterative procedure for computing optimal controls in linear systems with convex cost functionals is presented. The procedure is based on an algorithm due to Gilbert [3] for minimizing a quadratic form on a convex set. Each step of the procedure makes use of an algorithm due to Neustadt and Paiewonsky [1] to solve a strictly linear optimal control problem.

Dynamic Inventory Models and Stochastic Programming

A wide class of single-product, dynamic inventory problems with convex cost functions and a finite horizon is investigated as a stochastic programming problem. When demands have finite discrete distribution functions, we show that the problem can be substantially reduced in size to a linear program with upper-bounded variables. Moreover, we show that the reduced problem has a network representation; thus network flow theory can be used for solving this class of problems. A consequence of this result is that, if we are dealing with an indivisible commodity, an integer solution of the dynamic inventory problem exists. This approach can be computationally attractive if the demands in different periods are correlated or if ordering cost is a function of demand.