We consider the problem of minimizing a continuously differentiable function of several variables subject to smooth nonlinear constraints. We assume that the first order derivatives of the objective function and of the constraints can be neither calculated nor approximated explicitly. Hence, every minimization procedure must use only a suitable sampling of the problem functions. These problems ...

We introduce an algorithm for solving nonlinear optimization problems with general equality and box constraints. The proposed algorithm is based on smoothing of the exact l1−penalty function and solving the resulting problem by any box-constraint optimization method. We introduce a general algorithm and present theoretical results for updating the penalty and smoothing parameter. We apply the a...

The paper concerns the study of tilt stability of local minimizers in standard problems of nonlinear programming. This notion plays an important role in both theoretical and numerical aspects of optimization and has drawn a lot of attention in optimization theory and its applications, especially in recent years. Under the classical Mangasarian–Fromovitz Constraint Qualification, we establish re...

dynamic economic load dispatch is one of the most important roles of power generation’s operation and control. it determines the optimal controls of production of generator units with predicted load demand over a certain period of time. economic dispatch at minimum production cost is one of the most important subjects in the power network’s operation, which is a complicated nonlinear constraine...

A self-adaptive fitness formulation is presented for solving constrained optimization problems. In this method, the dimensionality of the problem is reduced by representing the constraint violations by a single infeasibility measure. The infeasibility measure is used to form a two-stage penalty that is applied to the infeasible solutions. The performance of the method has been examined by its a...

We study the problem of asset and liability management of participating insurance policies with guarantees. We develop a scenario optimization model for integrative asset and liability management, analyze the tradeoffs in structuring such policies, and study alternative choices in funding them. The nonlinearly constrained optimization model can be linearized through closed form solutions of the...

In a two-market genetic algorithm applied to a constrained optimization problem, two ‘markets’ are maintained. One market establishes fitness in terms of the objective function only; the other market measures fitness in terms of the problem constraints only. Previous work on knapsack problems has shown promise for the two-market approach. In this paper we: (1) extend the investigation of two-ma...

in recent years, wavelet packet modulation ofdm (wpm-ofdm) signals have been introduced for radar applications. these signals have important properties such as inherent high range resolution and high resistance of radar system against jamming reception. this paper investigates the problem of designing these family of signals according to the following criteria: constrained maximization of the d...

This paper proposes a generalized framework with joint normalization which learns lower-dimensional subspaces with maximum discriminative power by making use of the Riemannian geometry. In particular, we model the similarity/dissimilarity between subspaces using various metrics defined on Grassmannian and formulate dimensionality reduction as a non-linear constraint optimization problem conside...

In this paper we present a Lagrange-multiplier formulation of discrete constrained optimization problems, the associated discrete-space first-order necessary and sufficient conditions for saddle points, and an efficient first-order search procedure that looks for saddle points in discrete space. Our new theory provides a strong mathematical foundation for solving general nonlinear discrete opti...