Basic Sciences Applications

A new theorem of alternatives leading to sufficient conditions for the superiorization guarantee question of Dynamic String-Averaging in the inconsistent case

Categories Basic Sciences Applications, Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization

We study the Superiorization Methodology (SM) in the context of the General Dynamic String-Averaging (GDSA) method in the inconsistent case (that is, where the input operators don’t have a common fixed point) which primarily aims at achieving convex feasibility while simultaneously reducing an objective function. In many scientific and real-world problems modeled as constrained minimization … Read more

On the boundedness of infinite products of relaxed projections: perturbations resilience and dynamic string-averaging

Categories Basic Sciences Applications, Convex Optimization, Infinite Dimensional Optimization Tags , , , , , , , , ,

Very recently (2026), Bauschke and Tung extended from finite- to infinite-dimensional Hilbert spaces a result published by Meshulam in 1996 (following an earlier result of Aharoni-Duchet-Wajnryb from 1984) regarding the boundedness of infinite products of relaxed projections onto a finite family of closed affine subspaces. In the present note we extend in various ways the … Read more

Constrained Enumeration of Lucky Tickets: Prime Digits, Uniqueness, and Greedy Heuristics

Categories Basic Sciences Applications, Optimization in Data Science

We revisit the classical Lucky Ticket (LT) enumeration problem, in which an even-digit number is called lucky if the sum of the digits of its first half equals to that of its second half. We introduce two new subclasses — SuperLucky Tickets (SLTs), where all digits are distinct, and LuckyPrime Tickets (LPTs), where all digits … Read more

Immunity to Increasing Condition Numbers of Linear Superiorization versus Linear Programming

Categories Basic Sciences Applications, Constrained Nonlinear Optimization, Linear Programming Tags , , , , , , ,

Given a family of linear constraints and a linear objective function one can consider whether to apply a Linear Programming (LP) algorithm or use a Linear Superiorization (LinSup) algorithm on this data. In the LP methodology one aims at finding a point that fulfills the constraints and has the minimal value of the objective function … Read more

Evolving Scientific Discovery by Unifying Data and Background Knowledge with AI Hilbert

Categories Basic Sciences Applications, Global Optimization Applications, Semi-definite Programming Tags , , ,

The discovery of scientific formulae that parsimoniously explain natural phenomena and align with existing background theory is a key goal in science. Historically, scientists have derived natural laws by manipulating equations based on existing knowledge, forming new equations, and verifying them experimentally. In recent years, data-driven scientific discovery has emerged as a viable competitor in … Read more

Switching Time Optimization for Binary Quantum Optimal Control

Categories (Mixed) Integer Nonlinear Programming, Basic Sciences Applications, Control Applications Tags , ,

Quantum optimal control is a technique for controlling the evolution of a quantum system and has been applied to a wide range of problems in quantum physics. We study a binary quantum control optimization problem, where control decisions are binary-valued and the problem is solved in diverse quantum algorithms. In this paper, we utilize classical … Read more

Polynomial argmin for recovery and approximation of multivariate discontinuous functions

Categories Basic Sciences Applications, Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , ,

We propose to approximate a (possibly discontinuous) multivariate function f(x) on a compact set by the partial minimizer arg min_y p(x,y) of an appropriate polynomial p whose construction can be cast in a univariate sum of squares (SOS) framework, resulting in a highly structured convex semidefinite program. In a number of non-trivial cases (e.g. when … Read more

Developments in mathematical algorithms and computational tools for proton CT and particle therapy treatment planning

Categories Basic Sciences Applications, Biomedical Applications, Constrained Nonlinear Optimization Tags , , , , , , , ,

We summarize recent results and ongoing activities in mathematical algorithms and computer science methods related to proton computed tomography (pCT) and intensitymodulated particle therapy (IMPT) treatment planning. Proton therapy necessitates a high level of delivery accuracy to exploit the selective targeting imparted by the Bragg peak. For this purpose, pCT utilizes the proton beam itself … Read more

Decision Intelligence for Nationwide Ventilator Allocation

Categories Applications - OR and Management Sciences, Basic Sciences Applications, Optimization of Simulated Systems Tags , , , ,

Many states in the U.S. have faced shortages of medical resources because of the surge in the number of patients suffering from COVID-19. As many projections indicate, the situation will be far worse in coming months. The upcoming challenge is not only due to the exponential growth in cases but also because of inherent uncertainty … Read more

Finding the strongest stable massless column with a follower load and relocatable concentrated masses

Categories Basic Sciences Applications, Nonsmooth Optimization Tags ,

We consider the problem of optimal placement of concentrated masses along a massless elastic column that is clamped at one end and loaded by a nonconservative follower force at the free end. The goal is to find the largest possible interval such that the variation in the loading parameter within this interval preserves stability of … Read more