Nonlinear Optimization – Page 2 – Optimization Online

Coordinate Optimality Reformulation for Mixed-Integer Convex Programs with Indicators

Published: 2026/08/02

(Mixed) Integer Nonlinear Programming, Quadratic Programming disjunctive optimization, indicator constraints, mixed-integer convex programming

We consider mixed-integer convex optimization problems in which binary indicators control continuous variables. We introduce the Coordinate Optimality Reformulation (CORe) framework, which augments standard indicator formulations by incorporating coordinate-wise optimality information. The resulting reformulations preserve global optimality while substantially improving branch-and-bound performance, particularly in sparse and structured settings where the coordinate-wise optimality conditions expose exploitable … Read more

A Quantum Optimization Framework for Data-Assimilation-Augmented Parameter Estimation

Published: 2026/07/30

Muhammad Jalil Ahmad

Combinatorial Optimization, Nonlinear Optimization, Unconstrained Optimization data assimilation, Nonlinear Dynamical Systems, parameter estimation, Quantum Optimization, QUBO

Parameter estimation is a fundamental challenge in the calibration of ordinary differential equation (ODE) models, where repeated numerical integration can lead to high computational cost. In this work, we investigate whether quantum algorithms can be leveraged to assist parameter estimation in nonlinear dynamical systems. We develop a hybrid classical–quantum framework that reformulates a data-assimilation-augmented parameter … Read more

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

Convexlikeness and Supportedness in Quadratic Multiobjective Optimization

Published: 2026/07/19

Multi-Criteria Optimization, Quadratic Programming convexlikeness, hidden convexity, multiobjective optimization, nonconvex optimization, nonconvex quadratic programming, s-lemma, supportedness, Weighted sum scalarization

This paper studies geometric and structural properties of quadratic multiobjective optimization problems. Thereby, a multiobjective optimization problem is called convexlike if the upper image, i.e., the image set plus the nonnegative orthant, is a convex set. Moreover, we say that a feasible point is supported in case it is a minimal solution of a weighted … Read more

Robust Chance-Constrained Optimization using a Continuous Parameter Space Wasserstein-2 Ambiguity Set of Gaussian Mixtures

Published: 2026/07/18

Shibshankar Dey

Nonlinear Optimization, Robust Optimization, Stochastic Programming chance constraint, Gaussian mixture model (GMM), optimal transport, out-of-sample performance, wasserstein distance

We study distributionally robust linear chance-constrained problems in which uncertainty is modeled by a Gaussian mixture model (GMM). Finite-support distributionally robust (FDR) formulations, widely used in data-driven robust optimization, robustify over empirical mixture support points and therefore primarily stress-test the fitted nominal mixture. This can be insufficient when service reliability depends on structural misspecification of … Read more

Tight Conic Relaxations for Rank-one Doubly Nonnegative Matrix Completion

Published: 2026/07/18

Cone Programming, Global Optimization Applications, Quadratic Programming quadratically constrained quadratic programming, Rank-one doubly nonnegative matrix completions, Rank-one solutions, Sparsity pattern of mathematical optimization problem., Tight conic relaxations

We study tight conic relaxations for a quadratically constrained quadratic programming (QCQP) formulation of rank-one doubly nonnegative (DNN) matrix completion. Motivated by sparse QCQPs whose lifted matrix variables include elements not directly specified by the objective or constraints, we interpret tightness as a rank-one completion property for the unspecified elements. For sparsity patterns whose blocks … Read more

Exploring polynomial models in the Search Step of Direct Multisearch

Published: 2026/07/14

Multi-Criteria Optimization, Nonlinear Optimization derivative-free optimization, direct-search methods, multiobjective optimization, Pareto front approximation, quadratic interpolation

Direct Multisearch (DMS) is a class of direct-search algorithms designed for multiobjective derivative-free optimization. Its framework consists of an optional search step and a poll step, the latter ensuring the corresponding theoretical convergence properties. Recently, a search strategy based on the minimization of quadratic polynomial models, constructed from previously evaluated points, was proposed to improve … Read more

Adaptive Scenario Partitioning for Stochastic Bilevel Linear Programs

Published: 2026/07/10

Francisco Jara

Bilevel Optimization, Constrained Nonlinear Optimization, Stochastic Programming Adaptive partitioning, Basis-aware refinement, computational optimization, Scenario aggregation, Stochastic bilevel programming

This paper develops an adaptive scenario partitioning approach for stochastic bilevel linear programs. The method extends the Adaptive Partitioning Method, originally designed for two-stage stochastic programs, to settings in which a leader makes a first-stage decision while anticipating scenario dependent optimal responses from a follower. The proposed approach solves a sequence of aggregated master problems … Read more