Applications – Science and Engineering – Page 2

Rooting Out Self-Intersection: An Algebraic Shape-Optimization Barrier

Published: 2026/09/06, Updated: 2026/09/25

Nima Kakhsaz Malayeri

Applications - Science and Engineering, Multidisciplinary Design Optimization, Nonlinear Optimization barrier penalty function, iterative linear algebra techniques, shape optimization, unconstrained minimization

Self-intersection is a fundamental feasibility constraint in shape optimization: a self-crossing boundary leaves its interior, normal field, and finite-element mesh ill-defined, yet most existing barriers rely on heuristic geometric-proximity measures rather than certifying self-intersection directly. We propose a self-intersection barrier grounded in algebraic detection. We derived two bivariate polynomials from a curve’s Fourier coefficients whose … Read more

An optimal orbit design for LISA

Published: 2026/09/03

Yaguang Yang

Constrained Nonlinear Optimization, Multidisciplinary Design Optimization, Optimization of Systems modeled by PDEs constrained nonlinear optimization, formation fly, optimal orbit design

The ESA/NASA joint LISA (laser interferometer space antenna) mission is designed to detect gravitational waves to perform gravitational astronomy. A key mission requirement is the maintenance of a three-spacecraft constellation in a near-equilateral triangular configuration with a prescribed inter-spacecraft separation. Existing approaches have addressed this problem using simplified dynamical models to enhance tractability; however, the … Read more

On the Equivalence of Monge and Kantarovich Problems in Discrete Optimal Transport

Published: 2026/09/01

Thirumulanathan Dhayaparan

Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Optimization of Systems modeled by PDEs

Consider a discrete optimal transport problem that has at least two consumers. We show that the Monge and Kantorovich versions of such a discrete optimal transport problem are equivalent for all cost functions if and only if the supply from all the suppliers are equal, and the demand from every consumer is an integral multiple … Read more

Combining Reinforcement Learning with Arc-search Interior-Point Method for Path Planning

Published: 2026/08/21

Yaguang Yang

Constrained Nonlinear Optimization, Control Applications, Nonlinear Optimization arc-search, nonlinear optimization, obstacle avoidance, Path planning

Path planning in environments containing obstacles has numerous practical applications. The problem is challenging because it is inherently nonlinear and nonconvex. Consequently, a variety of techniques have been developed to address this problem, among which machine learning and optimal control (or optimization) have emerged as two prominent approaches. In general, machine learning methods do not … Read more

A Decision-Support Framework for Structuring and Reducing Large Multi-Objective Solution Sets via Clustering: An Application to Proton Therapy

Published: 2026/08/17

Nicole Cristina Cassimiro

(Mixed) Integer Linear Programming, Biomedical Applications, Multi-Criteria Optimization clustering, decision support, extended goal programming, goal programming, intensity modulated proton therapy, multi-criteria decision analysis, multi-objective optimization, multiobjective optimization, OR for medicine, Pareto set reduction, radiotherapy treatment planning, representative selection.

This paper proposes a four-stage decision-support framework for structuring and reducing large multi-objective solution sets into compact and interpretable collections of representative alternatives. The methodology combines: (Phase 1) systematic solution generation through extended goal programming and structured preference exploration; (Phase 2) robustness-aware enrichment and profiling under weight sensitivity analysis; (Phase 3) filtering and dominance-based reduction … Read more

Indicator Cuts for Benders Decomposition with Mixed-Integer Subproblems

Published: 2026/08/14

(Mixed) Integer Linear Programming, Energy, Polyhedra District energy system, generalized benders decomposition, Mixed-integer subproblem, non-convex cut formulation, Subproblem monotonicity

Classical Benders decomposition fails when the subproblem is a mixed-integer program, due to the absence of strong duality. We propose a novel class of dual-free indicator cuts that are applicable to all Benders-decomposable problems with a pure-integer master problem and mixed-integer linear programming (MILP) subproblems. These cuts are derived from the monotonicity property of the … Read more

Stochastic Heterogeneous Fleet Scheduling for Airport Ground Transportation under Passenger Spillover and Service Constraints

Published: 2026/08/10

(Mixed) Integer Linear Programming, Airline Optimization, Applications - OR and Management Sciences, Facility Planning and Design, Stochastic Programming airport management, Mobility, public transportation networks, stochastic optimization

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A Data-Assimilation-Augmented Optimization Framework for Parameter Estimation in Dynamical Systems

Published: 2026/07/29

Muhammad Jalil Ahmad

Control Applications, Nonlinear Optimization, Nonsmooth Optimization data assimilation, dynamical systems, inverse problems, nonlinear optimization, parameter estimation

Parameter estimation in nonlinear dynamical systems from observational data is a fundamental inverse problem with applications in many disciplines such as epidemiology, systems biology, climate science, and related fields. In practice, this is further complicated by the fact that observational data are often noisy, sparse, and available only for a subset of the state variables. … Read more

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

Published: 2026/07/29

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

Published: 2026/07/29

Basic Sciences Applications, Convex Optimization, Infinite Dimensional Optimization Affine subspace, boundedness, control, dynamic string-averaging, half-space, infinite product, innately regular, perturbation resilience, relaxed projection, strongly nonexpansive mapping

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