In this note, we revisit the classical first order necessary condition in mathematical programming in infinite dimension. We show that existence of Lagrange-Karush-Kuhn-Tucker multipliers is equivalent to the existence of an error bound for the constraint set, and is also equivalent to a generalized Abadie’s qualification condition. These results extend widely previous one like by … Read more
This work describes the application of a direct search method to the optimization of problems of real industrial interest, namely three new material science applications designed with the FactSage software. The search method is BiMADS, the biobjective version of the mesh adaptive direct search (MADS) algorithm, designed for blackbox optimization. We give a general description … Read more
In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that only stochastic information of the gradients of the objective function is available via a stochastic first-order oracle (SFO). Firstly, we propose a general framework of stochastic quasi-Newton methods for solving nonconvex stochastic optimization. The proposed framework extends the classic … Read more
Given a short term mining plan, the task for an operational mine planner is to determine how the equipment in the mine should be used each day. That is, how crushers, loaders and trucks should be used to realise the short term plan. It is important to achieve both grade targets (by blending) and maximise … Read more
In a recent paper (Cartis, Gould and Toint, Math. Prog. A 144(1-2) 93–106, 2014), the evaluation complexity of an algorithm to find an approximate first-order critical point for the general smooth constrained optimization problem was examined. Unfortunately, the proof of Lemma 3.5 in that paper uses a result from an earlier paper in an incorrect … Read more
The worst-case behaviour of a general class of regularization algorithms is considered in the case where only objective function values and associated gradient vectors are evaluated. Upper bounds are derived on the number of such evaluations that are needed for the algorithm to produce an approximate first-order critical point whose accuracy is within a user-defined … Read more
We present a solution algorithm for problems from steady-state gas transport optimization. Due to nonlinear and nonconvex physics and engineering models as well as discrete controllability of active network devices, these problems lead to hard nonconvex mixed-integer nonlinear optimization models. The proposed method is based on mixed-integer linear techniques using piecewise linear relaxations of the … Read more
In this paper we deal with the semivectorial bilevel problem in the Riemannian setting. The upper level is a scalar optimization problem to be solved by the leader, and the lower level is a multiobjective optimization problem to be solved by several followers acting in a cooperative way inside the greatest coalition and choosing among … Read more
We suggest a modification of the descent splitting methods for decomposable composite optimization problems, which maintains the basic convergence properties, but enables one to reduce the computational expenses per iteration and to provide computations in a distributed manner. It consists in making coordinate-wise steps together with a special threshold control. Citation Kazan Federal University, Kazan … Read more
The worst case complexity of direct-search methods has been recently analyzed when they use positive spanning sets and impose a sufficient decrease condition to accept new iterates. Assuming that the objective function is smooth, it is now known that such methods require at most O(n^2 epsilon^{-2}) function evaluations to compute a gradient of norm below … Read more