Related papers: Continuity conditions weaker than lower semi-conti…

Motivated by the grid search method and Bayesian optimization, we introduce the concept of contractibility and its applications in model-based optimization. First, a basic framework of contraction methods is established to construct a…

In the present paper we study necessary and sufficient conditions for the existence of a semicontinuous and finite Richter-Peleg multi-utility for a preorder. It is well know that, given a preorder on a topological space, if there is a…

Slater's condition -- existence of a "strictly feasible solution" -- is a common assumption in conic optimization. Without strict feasibility, first-order optimality conditions may be meaningless, the dual problem may yield little…

Recently ({\em Class. Quant. Grav.} {\bf 20} 625-664) the concept of {\em causal mapping} between spacetimes --essentially equivalent in this context to the {\em chronological map} one in abstract chronological spaces--, and the related…

This paper introduces the concept of Transient Slack Capability (TSC), a set of three necessary device-level conditions to ensure stability under sustained power perturbations. TSC states that a device must (1) possess sufficient stored…

In this paper, we develop new optional stopping theorems for scenarios where the stopping rules are defined by bounded continuity regions. Moreover, we establish a wide variety of inequalities on the supremums and infimums of functions of…

In this workshop, we present a compact but rigorous introduction to second-order optimality conditions for mathematical programs with equilibrium constraints (MPECs). We start from the classical nonlinear programming template, then explain…

This paper explores some sufficient conditions for the enhanced solvability of strong vector equilibrium problems, which can be established via a variational approach. Enhanced solvability here means existence of solutions, which are strong…

In this paper we study sufficient conditions for metric subregularity of a set-valued map which is the sum of a single-valued continuous map and a locally closed subset. First we derive a sufficient condition for metric subregularity which…

Weak supersolutions to the porous medium equation are defined by means of smooth test functions under an integral sign. We show that nonnegative weak supersolutions become lower semicontinuous after redefinition on a set of measure zero.…

We extend known existence and uniqueness results of weak measure solutions for systems of non-local continuity equations beyond the usual Lipschitz regularity. Existence of weak measure solutions holds for uniformly continuous vector fields…

We analyse various structural and order-theoretical aspects of abstract separation systems and partial lattices, as well as the relationship between the different submodularity conditions one can impose on them.

In today's global economy, supply chain (SC) entities have become increasingly interconnected with demand and supply relationships due to the need for strategic outsourcing. Such interdependence among firms not only increases efficiency but…

The addition of lower level integrality constraints to a bi-level linear program is known to result in significantly weaker analytical properties. Most notably, the upper level goal function in the optimistic setting lacks lower…

We study the semicontinuity of automorphism groups for perturbations of domains in complex space or in complex manifolds. We provide a new approach to the study of such results for domains having minimal boundary smoothness. The emphasis in…

We study the relationship between the partially synchronous state and the coupling structure in general dynamical systems. Our results show that, on the contrary to the widely accepted concept, topological symmetry in a coupling structure…

In high-stakes engineering applications, optimization algorithms must come with provable worst-case guarantees over a mathematically defined class of problems. Designing for the worst case, however, inevitably sacrifices performance on the…

Let $X$ and $Y$ be topological spaces, let $Z$ be a metric space, and let $f: X\times Y\to Z$ be a mapping. It is shown that when $Y$ has a countable base $\mathcal B$, then under a rather general condition on the set-valued mappings $X\ni…

We explore generalizations of some integrated learning and optimization frameworks for data-driven contextual stochastic optimization that can adapt to heteroscedasticity. We identify conditions on the stochastic program, data generation…

Large language models (LLMs) exhibiting test-time scaling behavior, such as extended reasoning traces and self-verification, have demonstrated remarkable performance on complex, long-term reasoning tasks. However, the robustness of these…