Journal•ISSN: 0233-1934

# Optimization

Taylor & Francis

About: Optimization is an academic journal published by Taylor & Francis. The journal publishes majorly in the area(s): Optimization problem & Variational inequality. It has an ISSN identifier of 0233-1934. Over the lifetime, 3473 publications have been published receiving 43558 citations.

Topics: Optimization problem, Variational inequality, Convex optimization, Convex analysis, Subderivative

##### Papers published on a yearly basis

##### Papers

More filters

••

TL;DR: The Kuhn-Tucker conditions of an optimization problem with inequality constraints are transformed equivalently into a special nonlinear system of equations T 0(z) = 0 as mentioned in this paper, and Newton's method for solving this system combines two valuable properties: the local Q-quadratic convergence without assuming the strict complementary slackness condition and the regularity of the Jacobian of T 0 at a point z under reasonable conditions.

Abstract: The Kuhn–Tucker conditions of an optimization problem with inequality constraints are transformed equivalently into a special nonlinear system of equations T 0(z) = 0. It is shown that Newton's method for solving this system combines two valuable properties: The local Q-quadratic convergence without assuming the strict complementary slackness condition and the regularity of the Jacobian of T 0 at a point z under reasonable conditions, so that Newton’s method can be used also far from a Kuhn–Tucker point

718 citations

••

TL;DR: In this paper, a unified fixed point theoretic framework is proposed to investigate the asymptotic behavior of algorithms for finding solutions to monotone inclusion problems, where the basic iterative scheme under consideration involves nonstationary compositions of perturbed averaged nonexpansive operators.

Abstract: A unified fixed point theoretic framework is proposed to investigate the asymptotic behavior of algorithms for finding solutions to monotone inclusion problems. The basic iterative scheme under consideration involves nonstationary compositions of perturbed averaged nonexpansive operators. The analysis covers proximal methods for common zero problems as well as for various splitting methods for finding a zero of the sum of monotone operators.

524 citations

••

TL;DR: In this bibliography main directions of research as well as main fields of applications of bilevel programming problems and mathematical programs with equilibrium constraints are summarized.

Abstract: In this bibliography main directions of research as well as main fields of applications of bilevel programming problems and mathematical programs with equilibrium constraints are summarized. Focus is also on the difficulties arising from nonuniqueness of lower-level optimal solutions and on optimality conditions.

463 citations

••

TL;DR: In this paper, an extension of the extragradient algorithm to equilibrium problems is presented, where the equilibrium bifunction is not required to satisfy any monotonicity property, but it must satisfy a certain Lipschitz-type condition.

Abstract: We make use of the auxiliary problem principle to develop iterative algorithms for solving equilibrium problems. The first one is an extension of the extragradient algorithm to equilibrium problems. In this algorithm the equilibrium bifunction is not required to satisfy any monotonicity property, but it must satisfy a certain Lipschitz-type condition. To avoid this requirement we propose linesearch procedures commonly used in variational inequalities to obtain projection-type algorithms for solving equilibrium problems. Applications to mixed variational inequalities are discussed. A special class of equilibrium problems is investigated and some preliminary computational results are reported. This article is dedicated to the Memory of W. Oettli.

320 citations