We study the complexity of a barrier method for linear-inequality constrained optimization problems where the objective function is only assumed to be analytic and convex. As a special case, we obtain the usual comple...
详细信息
We study the complexity of a barrier method for linear-inequality constrained optimization problems where the objective function is only assumed to be analytic and convex. As a special case, we obtain the usual complexity bounds for the linear programming problem and for when the objective function is convex and quadratic. (C) 1999 Academic Press.
Lagrangean dualization and subgradient optimization techniques are frequently used within the field of computational optimization for finding approximate solutions to large, structured optimization problems. The dual ...
详细信息
Lagrangean dualization and subgradient optimization techniques are frequently used within the field of computational optimization for finding approximate solutions to large, structured optimization problems. The dual subgradient scheme does not automatically produce primal feasible solutions;there is an abundance of techniques for computing such solutions (via penalty functions, tangential approximation schemes, or the solution of auxiliary primal programs), all of which require a fair amount of computational effort. We consider a subgradient optimization scheme applied to a Lagrangean dual formulation of a convex program, and construct, at minor cost, an ergodic sequence of subproblem solutions which converges to the primal solution set. Numerical experiments performed on a traffic equilibrium assignment problem under road pricing show that the computation of the ergodic sequence results in a considerable improvement in the quality of the primal solutions obtained, compared to those generated in the basic subgradient scheme.
We adapt some randomized algorithms of Clarkson [3] for linear programming to the framework of so-called LP-type problems, which was introduced by Sharir and Welzl [10]. This framework is quite general and allows a un...
详细信息
We adapt some randomized algorithms of Clarkson [3] for linear programming to the framework of so-called LP-type problems, which was introduced by Sharir and Welzl [10]. This framework is quite general and allows a unified and elegant presentation and analysis. We also show that LP-type problems include minimization of a convex quadratic function subject to convex quadratic constraints as a special case, for which the algorithms can be implemented efficiently, if only linear constraints are present. We show that the expected running times depend only linearly on the number of constraints, and illustrate this by some numerical results. Even though the framework of LP-type problems may appear rather abstract at first, application of the methods considered in this paper to a given problem of that type is easy and efficient. Moreover, our proofs are in fact rather simple, since many technical details of more explicit problem representations are handled in a uniform manner by our approach. In particular, we do not assume boundedness of the feasible set as required in related methods.
A polynomial approach is pursued For locally stabilizing discrete-time linear systems subject to input constraints. Using the Youla-Kucera parametrization and geometric properties of polyhedra and ellipsoids, the prob...
详细信息
A polynomial approach is pursued For locally stabilizing discrete-time linear systems subject to input constraints. Using the Youla-Kucera parametrization and geometric properties of polyhedra and ellipsoids, the problem of simultaneously deriving a stabilizing controller and the corresponding stability region is cast into standard convex optimization problems solved by linear, second-order cone and semidefinite programming. Key topics are touched on such as stabilization of multi-input multi-output plants or maximization of the size of the stability domain. Readily implementable algorithms are described. (C) 2001 Elsevier Science Ltd. All rights reserved.
We characterize the convex envelope of a given function f as the unique solution of a convex programming problem. It allows us to build a sequence of convex and polygonal function u(n) that converges uniformly to the ...
详细信息
We characterize the convex envelope of a given function f as the unique solution of a convex programming problem. It allows us to build a sequence of convex and polygonal function u(n) that converges uniformly to the convex envelope off.
This paper investigates a search problem for a moving target in which a searcher can anticipate the probabilities of routes selected by the target but does not have any time information about when the target tr transi...
详细信息
This paper investigates a search problem for a moving target in which a searcher can anticipate the probabilities of routes selected by the target but does not have any time information about when the target tr transits the route. If the searcher had some time information, he could develop an efficient search plan by varying allocations of search effort based on time. Due to the lack of time information, the searcher must ambush the target by distributing search effort to places where the target is likely to pass. There are few papers that deal mathematically with this type of search problem with no time information. Employing the criterion of detection probability, we formulate the problem and obtain necessary and sufficient conditions for the optimal solution. By applying the conditions, we propose two methods for solving the problem. The convex programming problem can be easily solved numerically by some well-known methods, e.g. the gradient projection method or the multiplier method. By numerical comparison, it is verified that the proposed methods have the excellent performance in computational time. We also elucidate some properties of the optimal distribution of search effort by some numerical examples. (C) 2001 Elsevier Science B.V. All rights reserved.
A sufficient LMI condition is proposed for checking robust stability of a polytope of polynomial matrices. It hinges upon two recent results: a new approach to polynomial matrix stability analysis and a new robust sta...
详细信息
A sufficient LMI condition is proposed for checking robust stability of a polytope of polynomial matrices. It hinges upon two recent results: a new approach to polynomial matrix stability analysis and a new robust stability condition for convex polytopic uncertainty. Numerical experiments illustrate that the condition narrows significantly the unavoidable gap between conservative tractable quadratic stability results and exact NP-hard robust stability results. (C) 2001 Elsevier Science Ltd. All rights reserved.
We consider the problem of determining whether or not a convex function f(x) is bounded below over R-n. Our focus is on investigating the properties of the vectors in the cone of recession 0(+) f of f(x) which are rel...
详细信息
We consider the problem of determining whether or not a convex function f(x) is bounded below over R-n. Our focus is on investigating the properties of the vectors in the cone of recession 0(+) f of f(x) which are related to the unboundedness of the function. (C) 2001 Elsevier Science B.V. All rights reserved.
A minimization problem with convex and separable objective function subject to a separable convex inequality constraint "less than or equal to" and bounded variables is considered. A necessary and sufficient...
详细信息
A minimization problem with convex and separable objective function subject to a separable convex inequality constraint "less than or equal to" and bounded variables is considered. A necessary and sufficient condition is proved for a feasible solution to be an optimal solution to this problem. convex minimization problems subject to linear equality/linear inequality "greater than or equal to" constraint, and bounds on the variables are also considered. A necessary and sufficient condition and a sufficient condition, respectively, are proved for a feasible solution to be an optimal solution to these two problems. Algorithms of polynomial complexity for solving the three problems are suggested and their convergence is proved. Some important forms of convex functions and computational results are given in the Appendix.
In this paper a proximal bundle method is introduced that is capable to deal with approximate subgradients. No further knowledge of the approximation quality (like explicit knowledge or controllability of error bounds...
详细信息
In this paper a proximal bundle method is introduced that is capable to deal with approximate subgradients. No further knowledge of the approximation quality (like explicit knowledge or controllability of error bounds) is required for proving convergence. It is shown that every accumulation point of the sequence of iterates generated by the proposed algorithm is a well-defined approximate solution of the exact minimization problem. In the case of exact subgradients the algorithm behaves like well-established proximal bundle methods. Numerical tests emphasize the theoretical findings.
暂无评论