Most research in robust optimization has so far been focused on inequality-only, convex conic programming with simple linear models for uncertain parameters. Many practical optimization problems, however, are nonlinear and non-convex. Even in linear programming, coefficients may still be nonlinear functions of uncertain parameters. In this paper, we propose robust formulations (see (1) versus (...

Abstract A basic framework for exploiting sparsity via positive semidefinite matrix completion is presented for an optimization problem with linear and nonlinear matrix inequalities. The sparsity, characterized with a chordal graph structure, can be detected in the variable matrix or in a linear or nonlinear matrix-inequality constraint of the problem. We classify the sparsity in two types, the...

The nonlinear complementarity problem has been used to study and formulate various equilibrium problems including the traffic equilibrium problem, the spatial equilibrium problem and the Nash equilibrium problem. To solve the nonlinear complementarity problem, various iterative methods such as projection methods, linearized methods and Newton method have been proposed and their convergence resu...

In this paper we analyze a nonlinear generalization of the Black-Scholes equation for pricing American style call option in which the volatility may depend on the underlying asset price and the Gamma of the option. We propose a novel method of pricing American style call options by means of transformation of the free boundary problem for a nonlinear Black-Scholes equation into the so-called Gam...

We present an accelerator scheme for use with existing packages that solve nonlinear programming problems with a large number of inequality constraints that arise in the process of discretizing continuous-time optimal control problems with state-space constraints. This scheme is based on the concept of outer approximations used in semi-infinite programming and acts as an external, active constr...

We construct non-linear information inequalities from Matúš’ infinite series of linear information inequalities. Each single non-linear inequality is sufficiently strong to prove that the closure of the set of all entropy functions is not polyhedral for four or more random variables, a fact that was already established using the series of linear inequalities. To the best of our knowledge, they ...

How does concern for consumption relative to others (”relativity”) affect the progressivity of the optimal income tax structure? In this paper we revisit this literature and present a more detailed analysis of the solution to the non-linear income tax problem with consumption interdependence than is currently available, generalizing some results and developing other results for cases with speci...

Siegenthaler proved that an n input 1 output, m-resilient (balanced mth order correlation immune) Boolean function with algebraic degree d satisfies the inequality : m + d ≤ n − 1. We provide a new construction method using a small set of recursive operations for a large class of highly nonlinear, resilient Boolean functions optimizing Siegenthaler’s inequality m + d = n − 1. Comparisons to pre...

In this work, we consider a generalized nonlinear variational-like inequality problem in the setting of locally convex topological vector spaces and prove the existence of its solutions. © 2005 Published by Elsevier Ltd MSC: 49J40; 47H19; 47H10