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Filter methods, introduced by Fletcher and Leyffer for nonlinear programming are characterized by the use of the dominance concept of multiobjective optimization, instead of a penalty parameter whose adjustment can be problematic. This paper presents a way to implement a filter based approach to solve a nonlinear bilevel programming problem in a linear approximations framework. The approach presented is based on the trust region idea from nonlinear programming, combined with filter-SQP algorithm, smooth and active sets techniques. The restoration procedure introduced in our algorithm consists in computing a rational solution. [ABSTRACT FROM AUTHOR]

This article discusses recent advances in mathematical modeling techniques of transmission networks and control devices within the scope of optimal power flow (OPF) implementations. Emphasis is on the newly proposed concept of representing meshed power networks using an extended conic quadratic (ECQ) model and its amenability to solution by using interior-point codes. Modeling of both classical power control devices and modern unified power flow controller (UPFC) technology is described in relation to the ECQ network format. Applications of OPF including economic dispatching, loss minimization, constrained power flow solutions, and transfer capability computation are presented. Numerical examples that can serve as testing benchmarks for future software developments are reported on a sample test network. [ABSTRACT FROM AUTHOR]

We consider optimization problems that can be formulated as minimizing the cost of a feasible solution wTx over an arbitrary combinatorial feasible set ]> . For these problems we describe a broad class of corresponding stochastic problems where the cost vector W has independent random components, unknown at the time of solution. A natural and important objective that incorporates risk in this stochastic setting is to look for a feasible solution whose stochastic cost has a small tail or a small convex combination of mean and standard deviation. Our models can be equivalently reformulated as nonconvex programs for which no efficient algorithms are known. In this paper, we make progress on these hard problems. Our results are several efficient general-purpose approximation schemes. They use as a black-box (exact or approximate) the solution to the underlying deterministic problem and thus immediately apply to arbitrary combinatorial problems. For example, from an available δ-approximation algorithm to the linear problem, we construct a δ(1 + ε)-approximation algorithm for the stochastic problem, which invokes the linear algorithm only a logarithmic number of times in the problem input (and polynomial in ]> ), for any desired accuracy level ε> 0. The algorithms are based on a geometric analysis of the curvature and approximability of the nonlinear level sets of the objective functions. [ABSTRACT FROM AUTHOR]

In this article, quadratic semiorthogonal B-spline scaling functions are developed to approximate the solutions of nonlinear Fredholm-Hammerstein integral equations. First, the quadratic B-spline scaling functions and their properties are presented; these properties are used to reduce the computation of integral equations to algebraic equations. [ABSTRACT FROM AUTHOR]

Novelty detection involves modeling the normal patterns for detecting any divergence from this behavior. Our recently proposed algorithm, Glabal&Local One Class Classifier (GLocal OCC), can solve this problem by maximizing the margin between the hyperplane and the origin through embedding the global information into the OCSVM framework. In this paper, we propose Linear Programming (LP) GLocal OCC (lpGLocal OCC) instead of the Quadratic Programming optimization to speed up GLocal OCC. By minimizing the average functional distance of the overall samples to the hyperplane, the lpGLocal OCC can attract the optimal hyperplane towards the centre of the data without using the origin anymore. Borrow off-the-shelf LP solver, this novel algorithm can be implemented easily and process solve large datasets rapidly. Results on benchmark datasets show that lpGLocal OCC not only has the comparable generalization power compared with the GLocal OCC besides its efficiency, but also has better generalization than (Ip)OCSVM due to its structured learning approach. [ABSTRACT FROM AUTHOR]

This paper presents a neurogenetic approach for solving nonlinear programming problems. Genetic algorithm must its popularity to make possible cover nonlinear and extensive search spaces. Neural networks with feedback connections provide a computing model capable of solving a large class of optimization problems. The association of a modified Hopfield network with genetic algorithm guarantees the convergence of the system to the equilibrium points, which represent feasible solutions for nonlinear programming problems. [ABSTRACT FROM AUTHOR]

Sensitivity-based strategies for on-line moving horizon estimation (MHE) and nonlinear model predictive control (NMPC) are presented both from a stability and computational perspective. These strategies make use of full-space interior-point nonlinear programming (NLP) algorithms and NLP sensitivity concepts. In particular, NLP sensitivity allows us to partition the solution of the optimization problems into background and negligible on-line computations, thus avoiding the problem of computational delay even with large dynamic models. We demonstrate these developments through a distributed polymerization reactor model containing around 10,000 differential and algebraic equations (DAEs). [ABSTRACT FROM AUTHOR]

Recent years have seen growth in the number of algorithms designed to solve challenging simulation-based nonlinear optimization problems. One such algorithm is the Trust-Region Parallel Direct Search (TRPDS) method developed by Hough and Meza. In this paper, we take advantage of the theoretical properties of TRPDS to make use of approximation models in order to reduce the computational cost of simulation-based optimization. We describe the extension, which we call mTRPDS, and present the results of a case study for two earth penetrator design problems. In the case study, we conduct computational experiments with an array of approximations within the mTRPDS algorithm and compare the numerical results to the original TRPDS algorithm and a trust-region method implemented using the speculative gradient approach described by Byrd, Schnabel, and Shultz. The results suggest new ways to improve the algorithm. [ABSTRACT FROM AUTHOR]

In this research, focusing on nonlinear integer programming problems, we propose an approximate solution method based on particle swarm optimization proposed by Kennedy et al. To be more specific, we develop a new particle swarm optimization method which is applicable to discrete optimization problems by incoporating a new method for generating initial search points, the rounding of values obtained by the move scheme and the revision of move methods. Furthermore, we show the efficiency of the proposed particle swarm optimization method by comparing it with an existing method through the application of them into the numerical examples. [ABSTRACT FROM AUTHOR]

This paper considers robust mean-variance portfolio selection problems including uncertainty sets and fuzzy factors. Since these problems are not well-defined problems due to fuzzy factors, it is hard to solve them directly. Therefore, introducing chance constraints, fuzzy goals and possibility measures, the proposed models are transformed into the deterministic equivalent problems. Furthermore, since it is difficult to solve them analytically and efficiently due to nonlinear programming problems, the solution method is constructed introducing a parameter and doing the equivalent transformations. [ABSTRACT FROM AUTHOR]

The problem of convexity runs deeply in economic theory. For example, increasing returns or upward slopes (convexity) and diminishing returns or downward slopes (concavity) of certain supply, demand, production and utility relations are often assumed in economics. Quite frequently, however, the observations have lost convexity (or concavity) due to errors of the measuring process. We derive the Karush- Kuhn-Tucker test statistic of convexity, when the convex estimator of the data minimizes the sum of squares of residuals subject to the assumption of non-decreasing returns. Testing convexity is a linear regression problem with linear inequality constraints on the regression coefficients, so generally the work of Gouriéroux, Holly and Monfort (1982) as well as Hartigan (1967) apply. Convex estimation is a highly structured quadratic programming calculation that is solved very efficiently by the Demetriou and Powell (1991) algorithm. Certain applications that test the convexity assumption of real economic data are considered, the results are briefly analyzed and the interpretation capability of the test is demonstrated. [ABSTRACT FROM AUTHOR]

Networks of coupled dynamical systems exhibit many interesting behaviours such as spatio-temporal chaos, pattern formation and synchronization. Such networks can be used to model a large variety of biological and physical systems. This contribution will focus on the 2-dimensional nonlinear map that describes the behaviour of individual neurons. The aim is to understand the coupling behaviour of this particular map and the dynamics of such coupled neuron systems. Various coupling schemes such as nearest neighbor coupling, random couplings and small-world networkings are numerically investigated. In particular, the paper will examine the transition of asynchronously firing neurons to a synchronous state. This is important in that it has similarities to the perceived behaviour of neurons in individuals during epileptic seizures. [ABSTRACT FROM AUTHOR]

According to the limitation of Principal Components Analysis in dealing with the nonlinear data, connecting with the Linear Programming Techniques for Multidimensional Analysis of Preference, this paper presents the Kernel Principal Components Analysis-Linear Programming Techniques for Multidimensional Analysis of Preference evaluation model. Kernel function maps linear inseparable input data into a high dimensional linear separable feature space via a nonlinear mapping technique. Then it carries on the linear principal components analysis in the high dimensional feature space. In addition, the weight of each index can be obtained in this model, thus it makes up another shortage of Principal Components Analysis. In the wastewater evaluation, the indices are numerous and the degree of correlation is not high, therefore, this model is more appropriate. Finally, this paper applies the model to the wastewater evaluation in Shanghai, and we obtain better evaluation results. [ABSTRACT FROM AUTHOR]

In recent years, a high speed and accurate optimization method has been expected for large scale nonlinear programming problems. As a new solution method for nonlinear programming problems, a particle swarm optimization (PSO) method was proposed by Kennedy et al. and has attracted considerable attention. However, there exist few reports with respect to successful results for constrained nonlinear programming problems by PSO-based methods. Furthermore, PSO-based methods have a shortcoming that the search is liable to stopping at a certain local solution. In this paper, incorporating the bisection method and a homomorphous mapping to carry out the search considering constraints as well as the multiple stretching technique and modified move schemes of particles to restraining the stopping around local solutions. Furthermore, we show the efficiency of the proposed revised PSO method (rPSO) by comparing it with an existing method through the application of them into the numerical examples. [ABSTRACT FROM AUTHOR]

This article discusses ability of Linear Programming models to be used as solvers of NP-complete problems. Integer Linear Programming is known as NP-complete problem, but non-integer Linear Programming problems can be solved in polynomial time, what places them in P class. During past three years there appeared some articles using LP to solve NP-complete problems. This methods use large number of variables (O(n9)) solving correctly almost all instances that can be solved in reasonable time. Can they solve infinitively large instances? This article gives answer to this question. [ABSTRACT FROM AUTHOR]

The article presents information on quadratic programming (QP). It deals with a special class of mathematical programs where a quadratic function of the decision variables needs to be optimized. QP has several types including unconstrained quadratic minimization problems, equality constrained quadratic minimization problems, and quadratic network optimization problems. QP can be used in finance, taxation, and equilibrium models.

The article provides information on parametric programming. Collection of data is significant in setting up a mathematical optimization model. Moreover, a postoptimal analysis consists of several analyses including sensitivity analysis (SA). A sort of extended SA is parametric programming. Meanwhile, in nonlinear programming, SA corresponds to perturbation analysis.

A definition of the term "nonlinear programming" is presented. The term refers to a collection of methodology associated with any optimization problem where nonlinear relationships may be present in the objective function or the constraints. Some examples of a linear programming problem are presented.

This encyclopedia entry presents information on multiobjective programming. It is related to linear, integer and nonlinear programming. Multiobjective programming deals with the extensions to theory and practice that enable knowledge workers and programmers to address mathematical programming problems with more than one objective function.

The article focuses on Knapsack problems with nonlinearities. It refers to nonlinear optimization problems with a single constraints. There are several applications for Knapsack problems with nonlinearities. Solution methods are used to solve such problems, which is further classified into continuous and integer convex problems, nonconvex problems and structured constraints. The formulas for the problems and solutions are provided.

The article discusses complementary problems. It refers to an inequality system and is linked to the Karush-Kuhn-Tucker necessary conditions of local optimality found in mathematical programming theory. A complementary problem can be linear or nonlinear. It presents algorithms for solving both types of complementary problems.

The article presents an encyclopedia entry for barrier functions and their modifications. In the middle of fifties and the early sixties, the use of barrier functions have been proposed for constrained optimization. The properties of modified barrier functions make them fundamentally different from the properties of barrier functions. The term is cross-referenced to computational complexity and nonlinear programming.

This article discusses the optimization problems involved in real-time control of systems with a human operator in the loop. Such real-time systems involve multiple objective functions, and there are multiple optimal solutions. Often these objectives are conflicting; an example is planning for contingencies as well as the base case. The solution to such multiobjective problems is typically a trade-off surface known as a Pareto surface whose axes are the various objective functions. The Pareto surface is to be presented to the human operator who will make the final decisions regarding control actions. Also, ideally the operator will be able to modify the parameters of the optimization process interactively to obtain desired results. Mathematical optimization techniques such as nonlinear programming have been used historically as the building blocks of real-time control systems.

A new method for minimization problem over simplex, as a generalization of a well-known in one-dimensional optimization bisection method is proposed. The convergence of the method for class of strictly unimodal functions including class of strictly convex functions is proved. The computational results are presented for a set of test problems. [ABSTRACT FROM AUTHOR]

The article presents an encyclopedia entry for calculus of variations. Many central ideas in optimization were first developed for the calculus of variations, then specialized to nonlinear programming. The most famous problem in the calculus of variations, called the Brachistochrone problem, was posed by John Bernoulli in 1696. The calculus of variations has influenced numerous areas of applied mathematics.

A definition of the term "Non-Linear Programming" is presented. Non-linear programming in mathematics concerns with the process of solving a system of equalities and inequalities over a set of unknown real variables, along with an objective function to be maximized or minimized.

The entry explains Wolfe's quadratic-programming problem algorithm. It is an adaptation of the simplex method that solves quadratic-programming problems with positive definite or positive semidefinite quadratic forms. This algorithm is based on the simultaneous solution of the linear constraints of the problems and associated Karush-Kuhn-Tucker conditions.

The article provides information on the restricted basis entry rule. The rule allows no more than two neighboring grid variables in an algorithmic solution for separable-programming problems. The restricted basis entry rule is also applied in solving quadratic-programming problems.

A definition of the term "quadratic-programming problem" is presented. It refers to a mathematical-programming problem with a quadratic objective function subject to a set of linear constraints.

A definition of the term "optimality criteria" is presented. There are mathematical formulas for many optimization problems by which one can test whether or not a given feasible solution is also optimal. The Karush-Kuhn-Tucker conditions is used for some nonlinear-programming problems while the simplex algorithm test is used for linear-programming problems.

A definition of the term "nonlinear goal programming" is presented. It is a goal programming methodology used to solve goal programming problems that have nonlinear elements in their model formulation.

A definition of the term "Lagrangian function" is presented. It refers to the mathematical-programming problem of minimizing function subject to a set of constraints. It makes use of Lagrange multipliers. The formula for the Lagrangian function is provided.

A definition of the term "Karush-Kuhn-Tucker conditions" is presented. It refers to the conditions that must be satisfied to solve a general nonlinear programming problem. It stipulates that the problem constraints must satisfy a regularity condition known as constraint qualification. In the linear programming problem, the conditions yield the complementary slackness conditions of the primal and dual problems.

A definition of "GRG method" as a gradient method and its relationship with quadratic programming is presented.