We bring together the theories of duality and dynamic programming. We show that the dual of an additively separable dynamic optimization problem can be recursively decomposed using summaries of past Lagrange multipliers as state variables. Analogous to the Bellman decomposition of the primal problem, we prove equality of values and solution sets for recursive and sequential dual problems. In no...

We introduce some methods for constrained nonlinear programming that are widely used in practice and that are known under the names SQP for sequential quadratic programming and SCP for sequential convex programming. In both cases, convex subproblems are formulated, in the first case a quadratic programming problem, in the second case a separable nonlinear program in inverse variables. The metho...

Abs t rac t We introduce some methods for constrained nonlinear programming that are widely used in practice and that are known under the names SQP for sequential quadratic programming and SCP for sequential convex programming. In both cases, convex subproblems are formulated, in the first case a quadratic programming problem, in the second case a separable nonlinear program in inverse variable...

We propose a polynomial algorithm for a separable convex optimization problem with linear constraints. We do not make any additional assumptions about the structure of the objective function except for polynomial computability. That is, the objective function can be non-differentiable. The running time of our algorithm is polynomial in the size of the input consisting of an instance of the prob...

The nonmonotone linear complementarity problem (LCP) is formulated as a bilinear program with separable constraintsand an objective function that minimizesa natural error residual for the LCP. A linear-programming-basedalgorithm applied to the bilinear program terminates in a nite number of steps at a solution or stationary point of the problem. The bilinear algorithm solved 80 consecutive case...

We discuss two models from the literature that have been developed to formulate piecewise linear approximations of separable nonlinear functions by way of mixed-integer programs. We show that the most commonly proposed method is computationally inferior to a lesser known technique by comparing analytically the linear programming relaxations of the two formulations. A third way of formulating th...

In this paper, the problem under consideration is multiobjective non-linear fractional programming problem involving semilocally convex and related functions. We have discussed the interrelation between the solution sets involving properly efficient solutions of multiobjective fractional programming and corresponding scalar fractional programming problem. Necessary and sufficient optimality...

The problem of inverting trained feedforward neural networks is to find the inputs which yield a given output. In general, this problem is an ill-posed problem because the mapping from the output space to the input space is a one-to-many mapping. In this paper, we present a method for dealing with the inverse problem by using mathematical programming techniques. The principal idea behind the me...