This paper is concerned with a class optimal switching nonsmoth optimal control problem is considered. Both the switching instants and the control function are to the chosen such that the cost functional is minimized.The necessary optimality conditions are derived by means of normal cone and Dubovitskii Milyutin theory. Citation Technical report 2007-3 Submited to the … Read more
A common method for constructing a function from a finite set of moments is to solve a constrained minimization problem. The idea is to find, among all functions with the given moments, that function which minimizes a physically motivated, strictly convex functional. In the kinetic theory of gases, this functional is the kinetic entropy; the … Read more
We provide and analyze a based average for two convex functions, based on a kernel function. It covers several known averages such as the arithmetic average, epigraphical average, and the proximal average. When applied to the Fitzpatrick function and the conjugate of Fitzpatrick function associated with a monotone operator, our average produces an autoconjugate (also … Read more
Shor’s r-algorithm is an iterative method for unconstrained optimization, designed for minimizing nonsmooth functions, for which its reported success has been considerable. Although some limited convergence results are known, nothing seems to be known about the algorithm’s rate of convergence, even in the smooth case. We study how the method behaves on convex quadratics, proving … Read more
Given $\cA := \{a^1,\ldots,a^m\} \subset \R^n$ and $\eps > 0$, we propose and analyze two algorithms for the problem of computing a $(1 + \eps)$-approximation to the radius of the minimum enclosing ball of $\cA$. The first algorithm is closely related to the Frank-Wolfe algorithm with a proper initialization applied to the dual formulation of … Read more
We consider the problem of minimizing the sum of a smooth function and a separable convex function. This problem includes as special cases bound-constrained optimization and smooth optimization with l_1-regularization. We propose a (block) coordinate gradient descent method for solving this class of nonsmooth separable problems. We establish global convergence and, under a local Lipschitzian … Read more
This paper focuses on monotone L\”{o}wner operators in Euclidean Jordan algebras and their applications to the symmetric cone complementarity problem (SCCP). We prove necessary and sufficient conditions for locally Lipschitz L\”{o}wner operators to be monotone, strictly monotone and strongly monotone. We also study the relationship between monotonicity and operator-monotonicity of L\”{o}wner operators. As a by-product … Read more
The goal of the current paper is to introduce the notion of certificates which verify the accuracy of solutions of computational problems with convex structure; such problems include minimizing convex functions, variational inequalities corresponding to monotone operators, computing saddle points of convex-concave functions and solving convex Nash equilibrium problems. We demonstrate how the implementation of … Read more
We propose a new iterative approach for solving linear programs over convex cones. Assuming that Slaters condition is satisfied, the conic problem is transformed to the minimization of a convex differentiable function. This “agumented primal-dual function” or “apd-function” is restricted to an affine set in the primal-dual space. The evaluation of the function and its … Read more
We study primal solutions obtained as a by-product of subgradient methods when solving the Lagrangian dual of a primal convex constrained optimization problem (possibly nonsmooth). The existing literature on the use of subgradient methods for generating primal optimal solutions is limited to the methods producing such solutions only asymptotically (i.e., in the limit as the … Read more