This paper presents a neural network approach for solving convex programming problems with equality constraints. After defining the energy function and neural dynamics of the proposed neural network, we show the exist...
详细信息
This paper presents a neural network approach for solving convex programming problems with equality constraints. After defining the energy function and neural dynamics of the proposed neural network, we show the existence of an equilibrium point at which the neural dynamics becomes asymptotically stable. It is shown that under proper conditions, an optimal solution of the underlying convex programming problems is an equilibrium point of the neural dynamics, and vise verse. The configuration of the proposed neural network with an exact layout is provided for solving linear programming problems. The operational characteristics of the neural network are demonstrated by numerical examples. (C) 1998 Elsevier Science Ltd. All rights reserved.
Sliding modes are used to analyze a class of dynamical systems that solve convex programming problems. The analysis is carried out using concepts from the theory of differential equations with discontinuous right-hand...
详细信息
Sliding modes are used to analyze a class of dynamical systems that solve convex programming problems. The analysis is carried out using concepts from the theory of differential equations with discontinuous right-hand sides and Lyapunov stability theory. It is shown that the equilibrium points of the system coincide with the minimizers of the convex programming problem, and that irrespective of the initial state of the system the state trajectory converges to the solution set of the problem. The dynamic behavior of the systems is illustrated by two numerical examples.
A cutting plane algorithm for minimizing a convex function subject to constraints defined by a separation oracle is presented. The algorithm is based on approximate analytic centers. The nonlinearity of the objective ...
详细信息
A cutting plane algorithm for minimizing a convex function subject to constraints defined by a separation oracle is presented. The algorithm is based on approximate analytic centers. The nonlinearity of the objective function is taken into account, yet the feasible region is approximated by a containing polytope. This containing polytope is regularly updated by adding a new cut through a test point. Each test point is an approximate analytic center of the intersection of a containing polytope and a level set of the nonlinear objective function. We establish the complexity of the algorithm. Our complexity estimate is given in terms of the problem dimension, the desired accuracy of an approximate solution, and other parameters that depend on the geometry of a specific instance of the problem.
We consider the volumetric cutting plane method for finding a point in a convex set C subset of R-n that is characterized by a separation oracle. We prove polynomiality of the algorithm with each added cut placed dire...
详细信息
We consider the volumetric cutting plane method for finding a point in a convex set C subset of R-n that is characterized by a separation oracle. We prove polynomiality of the algorithm with each added cut placed directly through the current point and show that this "central cut" version of the method can be implemented using no more than 25n constraints at any time.
In this paper, an unconstrained convex programming dual approach for solving a class of linear semi-infinite programming problems is proposed. Both primal and dual convergence results are established under some basic ...
详细信息
In this paper, an unconstrained convex programming dual approach for solving a class of linear semi-infinite programming problems is proposed. Both primal and dual convergence results are established under some basic assumptions. Numerical examples are also included to illustrate this approach.
In this report the problem of minimization of a convex function f ( x ) on a convex closed and bounded set Q ⊂ R n is considered. The method described below concerns gradient methods of the search of extremum of conve...
详细信息
In this report the problem of minimization of a convex function f ( x ) on a convex closed and bounded set Q ⊂ R n is considered. The method described below concerns gradient methods of the search of extremum of convex functions. The discrete analogue of the approximation gradient plays here the role of the gradient (Batukhtin and Maiboroda, 1984; Batukhtin and Maiboroda, 1995).
The aim of this paper is to carry out an exhaustive post optimization analysis in a convex Goal programming problem, so as to study the possible existence of satisfying solutions for different levels of the target val...
详细信息
The aim of this paper is to carry out an exhaustive post optimization analysis in a convex Goal programming problem, so as to study the possible existence of satisfying solutions for different levels of the target values. To this end, an interactive algorithm is proposed, which allows us to improve the values of the objective functions, after obtaining a satisfying solution, if such a solution exists, in such a way that a Pareto optimal solution is finally reached, through a successive actualization of such target values. This way, the target values are lexicographically improved, according to the priority order previously given by the decision maker, in an attempt to harmonize the concepts of satisfying and efficient solutions, which have traditionally been in conflict. (C) 1998 Elsevier Science B.V.
This paper presents a new interior point algorithrn for linearly constrainedconvex programming which is based upon interior ellipsoid mehtod- It is shown thatthe method is a polynomial time algorithm.
This paper presents a new interior point algorithrn for linearly constrainedconvex programming which is based upon interior ellipsoid mehtod- It is shown thatthe method is a polynomial time algorithm.
We give efficiency estimates for proximal bundle methods for finding f* := min(x)f, where f and X are convex. We show that, for any accuracy epsilon>0, these methods find a point x(k) is an element of X such that f...
详细信息
We give efficiency estimates for proximal bundle methods for finding f* := min(x)f, where f and X are convex. We show that, for any accuracy epsilon>0, these methods find a point x(k) is an element of X such that f(x(k)) - f* less than or equal to epsilon after at most k = O (1/epsilon(3)) objective and subgradient evaluations.
A general approach to analyze convergence of the proximal-like methods for variational inequalities with set-valued maximal monotone operators is developed. It is oriented to methods coupling successive approximation ...
详细信息
A general approach to analyze convergence of the proximal-like methods for variational inequalities with set-valued maximal monotone operators is developed. It is oriented to methods coupling successive approximation of the variational inequality with the proximal point algorithm as well as to related methods using regularization on a subspace and weak regularization. This approach also covers so-called multistep regularization methods, in which the number of proximal iterations in the approximated problems is controlled by a criterion characterizing these iterations as to be effective. The conditions on convergence require control of the exactness of the approximation only in a certain region of the original space. Conditions ensuring linear convergence of the methods are established.
暂无评论