A primal-infeasible interior point algorithm for linearly constrained convex programming
A proximal point method for nonsmooth convex optimization problems in Banach spaces.
A proximal regularization of the steepest descent method
A PVT-Type Algorithm for Minimizing a Nonsmooth Convex Function
2000 Mathematics Subject Classification: 90C25, 68W10, 49M37.A general framework of the (parallel variable transformation) PVT-type algorithm, called the PVT-MYR algorithm, for minimizing a non-smooth convex function is proposed, via the Moreau-Yosida regularization. As a particular scheme of this framework an ε-scheme is also presented. The global convergence of this algorithm is given under the assumptions of strong convexity of the objective function and an ε-descent condition determined by an...
A Recession Notion for a Class of Monotone Bivariate Functions
Using monotone bifunctions, we introduce a recession concept for general equilibrium problems relying on a variational convergence notion. The interesting purpose is to extend some results of P. L. Lions on variational problems. In the process we generalize some results by H. Brezis and H. Attouch relative to the convergence of the resolvents associated with maximal monotone operators.
A Regularized Continuous Linearization Method of the Fourth Order
A second-order stochastic dominance portfolio efficiency measure
In this paper, we introduce a new linear programming second-order stochastic dominance (SSD) portfolio efficiency test for portfolios with scenario approach for distribution of outcomes and a new SSD portfolio inefficiency measure. The test utilizes the relationship between CVaR and dual second-order stochastic dominance, and contrary to tests in Post [Post] and Kuosmanen [Kuosmanen], our test detects a dominating portfolio which is SSD efficient. We derive also a necessary condition for SSD efficiency...
A sequential iteration algorithm with non-monotoneous behaviour in the method of projections onto convex sets
The method of projections onto convex sets to find a point in the intersection of a finite number of closed convex sets in a Euclidean space, may lead to slow convergence of the constructed sequence when that sequence enters some narrow “corridor” between two or more convex sets. A way to leave such corridor consists in taking a big step at different moments during the iteration, because in that way the monotoneous behaviour that is responsible for the slow convergence may be interrupted. In this...
A smoothing Newton method for the second-order cone complementarity problem
In this paper we introduce a new smoothing function and show that it is coercive under suitable assumptions. Based on this new function, we propose a smoothing Newton method for solving the second-order cone complementarity problem (SOCCP). The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. It is shown that any accumulation point of the iteration sequence generated by the proposed algorithm is a solution to the SOCCP. Furthermore,...
A Stable Interior Penalty Method for Convex Extremal Problems.
A Trust Region Method Using Subgradient for Minimizing a Nondifferentiable Function
Absolute minimizer in convex programming by exponential penalty.
Algorithms construction for variational inequalities.
An adaptive parallel projection method for solving convex feasibility problems.
An Algorithm for Calculating One Subgradient of a Convex Function of Two Variables.
An Algorithm for Discrete Linear Lp Approximation.
An algorithm of successive minimization in convex programming
An analytic center cutting plane algorithm for finding equilibrium points
We present a variant of the analytic center cutting plane algorithm proposed by Goffin et al. (1996) to approximately solve equilibrium problems as proposed by Blum and Oettli (1994), which include as particular problems the variational inequalities problem, the Nash equilibria problem in non-cooperative games, the convex minimization problem, and the fixed point problem. Furthermore, we analyze the convergence and complexity of the modified algorithm.
An application of conjugate duality for numerical solution of continuous convex optimal control problems
An application of the Hahn-Banach theorem in convex analysis