Kuhn-Tucker points play a fundamental role in the analysis and the numerical solution of monotone inclusion problems, providing in particular both primal and dual solutions. We propose a class of strongly convergent algorithms for constructing the best approximation to a reference point from the set of Kuhn-Tucker points of a general Hilbertian composite monotone inclusion problem. Applications...

We consider a class of constrained optimization problems where the objective function is a sum of a smooth function and a nonconvex non-Lipschitz function. Many problems in sparse portfolio selection, edge preserving image restoration and signal processing can be modelled in this form. First we propose the concept of the Karush-Kuhn-Tucker (KKT) stationary condition for the non-Lipschitz proble...

The Kuhn-Tucker model provides a utility theoretic framework for estimating preferences over commodities for which individuals choose not to consume one or more of the goods. This paper provides an application of the Kuhn-Tucker model to the problem of recreation demand and site selection, modeling the demand for fishing in the Wisconsin Great Lakes region. Disciplines Agricultural and Resource...

Introduction. In two previous notes [9],1 I stated some results which, in a general way, may be expressed as follows: If the Taylor series which represents an entire function satisfies a certain gap condition (which depends only on the order of F(z)), the zeros of F(z) —f(z) are not exceptional with respect to the proximate order of F(z) by any meromorphic function f(z) ^ w of lower order. On t...

This paper is devoted to studying the robust isolated calmness of the Karush– Kuhn–Tucker (KKT) solution mapping for a large class of interesting conic programming problems (including most commonly known ones arising from applications) at a locally optimal solution. Under the Robinson constraint qualification, we show that the KKT solution mapping is robustly isolated calm if and only if both t...

Stability properties of the problem of minimizing a (nonconvex) linear-quadratic function over an Euclidean ball, known as the trust-region subproblem, are studied in this paper. We investigate in detail the case where the linear part of the objective function is perturbed and obtain necessary and sufficient conditions for the upper/lower semicontinuity of the Karush-Kuhn-Tucker point set map a...

The Kuhn-Tucker model of Wales and Woodland (1983) provides a utility theoretic framework for estimating preferences over commodities for which individuals choose not to consume one or more of the goods. Due to the complexity of the model, however, there have been few applications in the literature and little attention has been paid to the problems of welfare analysis within the Kuhn-Tucker fra...

This paper proposes strategic biddings for a consumer demand that participates in both the day-ahead and balancing markets. The behavior of is represented by bilevel optimization programming with minimization costs at upper level (UL) subject to co-optimization energy reserve market clearing process lower problem (LL). Using Karush-Kuhn-Tucker (KKT) optimality constraints replace LL problem, mo...

Each member  ∈ [1 ] chooses her level of  ≥ 0 to maximize her utility  = √− P  6= −  a function that is twice-differentiable and concave. Assuming  ≥ 0 to be the Lagrangian parameters, the optimal level of   #   satisfies the necessary and sufficient first-order conditions  1 2 − 1 2  −  +  = 0 and the Kuhn-Tucker conditions  = 0 for any  ∈ [1  ], thus ...

A finite-time attitude compensation control scheme is developed for an over-activated rigid spacecraft subject to actuator faults, misalignment, external disturbances and uncertain inertia parameters. The controller is synthesised based on the sliding mode control theory, and guarantees the finite-time reachability of the system states. A sufficient condition for the controller to accommodate m...