Journal of Optimization Theory and Applications
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Approximate solution of a class of singular control problems
Journal of Optimization Theory and Applications - Tập 13 - Trang 461-483 - 1974
A class of singular control problems involving amplitude constraints on the controls is examined. IfL
∞ is the space of control functionsU, the control constraint setS can be identified with the unit ball inL
∞. Now, for anyn ∈ (1, ∞), an analogous problem may be set up withL
n
forU and the unit ball inL
n
forS. This modified ......
On Higher-Order Sensitivity Analysis in Nonsmooth Vector Optimization
Journal of Optimization Theory and Applications - Tập 162 - Trang 463-488 - 2013
We propose the notion of higher-order radial-contingent derivative of a set-valued map, develop some calculus rules and use them directly to obtain optimality conditions for several particular optimization problems. Then we employ this derivative together with contingent-type derivatives to analyze sensitivity for nonsmooth vector optimization. Properties of higher-order contingent-type derivative......
Nearest q-Flat to m Points
Journal of Optimization Theory and Applications - Tập 105 - Trang 249-252 - 2000
Recently, Bradley and Mangasarian studied the problem of finding the nearest plane to m given points in ℝn in the least square sense. They showed that the problem reduces to finding the least eigenvalue and associated eigenvector of a certain n×n symmetric positive-semidefinite matrix. We extend this result to the general problem of finding the nearest q-flat to m points, with 0≤q≤n−1.
Infinite-Horizon Stochastic Differential Games with Branching Payoffs
Journal of Optimization Theory and Applications - Tập 111 - Trang 445-460 - 2001
In this paper, we consider infinite-horizon stochastic differential games with an autonomous structure and steady branching payoffs. While the introduction of additional stochastic elements via branching payoffs offers a fruitful alternative to modeling game situations under uncertainty, the solution to such a problem is not known. A theorem on the characterization of a Nash equilibrium solution f......
Partial differential equations and finite-difference methods in image processing, part 1: Image representation
Journal of Optimization Theory and Applications - Tập 23 - Trang 65-91 - 1977
Stochastic representation of discrete images by partial differential equation operators is considered. It is shown that these representations can fit random images, with nonseparable, isotropic covariance functions, better than other common covariance models. Application of these models in image restoration, data compression, edge detection, image synthesis, etc., is possible. Different representa......
Geometrical characterization of weakly efficient points
Journal of Optimization Theory and Applications - Tập 90 - Trang 217-223 - 1996
In this note, we present a geometrical characterization of the set of weakly efficient points in constrained convex multiobjective optimization problems, valid for a compact set of objectives.
Numerical solution of a time-optimal parabolic boundary-value control problem
Journal of Optimization Theory and Applications - Tập 27 Số 2 - Trang 271-290 - 1979
Infimal Convolution and Duality in Problems with Third-Order Discrete and Differential Inclusions
Journal of Optimization Theory and Applications - Tập 184 - Trang 781-809 - 2020
This paper is concerned with the Mayer problem for third-order evolution differential inclusions; to this end, first we use auxiliary problems with third-order discrete and discrete-approximate inclusions. In the form of Euler–Lagrange-type inclusions and transversality conditions, necessary and sufficient optimality conditions are derived. The principal idea of obtaining optimal conditions is loc......
Asymptotic Analysis of Linear Feedback Nash Equilibria in Nonzero-Sum Linear-Quadratic Differential Games
Journal of Optimization Theory and Applications - Tập 101 - Trang 693-722 - 1999
In this paper, we discuss nonzero-sum linear-quadratic differential games. For this kind of games, the Nash equilibria for different kinds of information structures were first studied by Starr and Ho. Most of the literature on the topic of nonzero-sum linear-quadratic differential games is concerned with games of fixed, finite duration; i.e., games are studied over a finite time horizon t
f. In th......
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