Nonsmooth nonconvex optimizationIn this paper, we focus on the problem of minimizing the sum of nonconvex smooth component functions and a nonsmooth weakly convex function composed with a linear operator. One specific application is logistic regression problems with weakly convex regularizers that ...
Characterization of (weakly/properly/robust) efficient solutions in nonsmooth semi-infinite multiobjective optimization using convexificatorsIn this note, by making use of the concept of unbounded approximate Hessian matrices, we present second order optimality conditions for a constrained mathematical ...
We give a short proof of Wolff–Denjoy theorem for (not necessarily smooth) strictly convex domains. With similar techniques we are also able to prove a Wolff–Denjoy theorem for weakly convex domains, again without any smoothness assumption on the boundary. Similar content being viewed by others...
In this paper, we establish a strong convergence theorem regarding a regularized variant of the projected subgradient method for nonsmooth, nonstrictly convex minimization in real Hilbert spaces. Only one projection step is needed per iteration and the involved stepsizes are controlled so that the alg...
Exploiting some tools of modern variational analysis involving the approximate extremal principle, the fuzzy sum rule for the Fréchet subdifferential, the sum rule for the limiting subdifferential and the scalarization formulae of the coderivatives, we establish necessary conditions for (weakly) efficient...
In this paper, we study a nonsmooth semi-infinite multi-objective E-convex programming problem involving support functions. We derive sufficient optimality conditions for the primal problem. We formulate Mond-Weir type dual for the primal problem and est
robust ϵ-quasi-(weakly) efficient solutionsrobust optimalityϵ-approximate condition of degree nϵ-vector duality of degree nrobust ϵ-Mond-Weir type duality of degree nϵ-approximate weak vector saddle-point of degree nWe introduce a new concept of generalized convexity of 'degree n ' ...
The vector optimization problem for the set-valued function is considered, where X0 is a subset of a real Banach space X and Y is a real Banach space with a given partial order defined by a convex, closed and pointed cone with nonempty interior C. Introducing two infinite elements ±∞C...
Weakly Convex Optimization over Stiefel Manifold Using Riemannian Subgradient-Type Methods We consider a class of nonsmooth optimization problems over the Stiefel manifold, in which the objective function is weakly convex in the ambient Euclidean... X Li,S Chen,Z Deng,... - 《Siam Journal on Opt...
Let us assume that a sequence {f n } n=1 ∞ of proper lower semicontinuous convex functions is bounded on some open subset of a weakly compactly generated Banach space. It is shown that if {f n } n=1 ∞ is a Mosco converging sequence, then for every subgradient x * of f at x ...