Global Optimization – Optimization Online

A Direction Adaptation Evaluation Strategy for Noisy Derivative-Free Optimization

Published: 2026/07/08

Global Optimization, Nonlinear Optimization Complexity Results, Direction Adaptation, evolution strategy, heuristic optimization, Noisy derivative-free optimization, randomized optimization

In this paper, we develop a direction adaptation evolution strategy (DAES)—a new MAES-type method—for noisy derivative-free optimization, designed to reconcile the population-based search mechanisms of evolution strategies with rigorous complexity analysis. Unlike standard MAES schemes, DAES fixes the adaptation matrix to the identity and replaces matrix adaptation with a structured direction-generation mechanism based on symmetric … Read more

Operation-Aware Deterministic Global Optimization of Carnot Battery Design using Hybrid Modeling

Published: 2026/06/30

Energy, Global Optimization Applications Combined optimization of design and operation, deterministic global optimization, Hybrid modeling, MAiNGO, Pumped thermal energy storage, Reduced space modeling

The global demand for grid-scale energy storage continues to increase. Carnot batteries (CBs) are not geographically constrained and consist of mature components. Furthermore, charging power, discharging power, and storage capacity can be sized independently and tailored to the intended use case. Designing an optimal CB also requires considering the resulting operational behavior. While design and … Read more

Advanced Geometrical Test for Interval Branch and Bound methods

Published: 2026/06/30

Global Optimization, Robust Optimization branch and bound method, Geometrical Test, global optimization, interval arithmetic, optimality conditions

The Interval Branch and Bound (IBB) method is a widely used approach for solving nonlinear programming problems, especially when a rigorous solution is required. It uses Interval Arithmetic to handle rounding errors. Although numerous variants of the IBB method have been proposed in the literature, relatively few implementations incorporate Karush-Kuhn-Tucker or Fritz-John (FJ) optimality conditions … Read more

Local-to-Global Exactness of SDP Relaxations for Sparse QCQPs

Published: 2026/06/19

Global Optimization Theory, Quadratic Programming, Semi-definite Programming block-clique sparsity, chordal graph, clique-wise formulation, exact SDP relaxation, local-to-global exactness, quadratically constrained quadratic program, rank-at-most-one optimal solution., semidefinite programming relaxation, sparse optimization

We study exact semidefinite programming (SDP) relaxation for a given sparse quadratically constrained quadratic program (QCQP). The SDP relaxation is exact if, whenever it has an optimal solution, it admits a rank-at-most-one optimal solution that corresponds to an optimal solution of the QCQP. Using the maximal cliques of a chordal extension of the aggregate sparsity … Read more

On exact copositive representation of simplicial quadratic optimization problems, their strong conic duality and a new proof of the Frank-Wolfe theorem

Published: 2026/06/16

Cone Programming, Global Optimization, Global Optimization Theory

We are interested in exactness, strong conic duality and dual attainability in copositive relaxations of quadratic optimization problems (QPs) of a special form, in which any (feasible) QP can be recast. By using our results, the celebrated Frank-Wolfe theorem on the attainability of any bounded QP even over unbounded polyhedra, regardless of whether the objective … Read more

Storage Participation in Electricity Markets: Time Discretization through Robust Optimization

Published: 2026/05/11

Energy, Global Optimization, Robust Optimization arbitrage, continuous-time linear programming, electricity storage, frequency regulation, nonconvex robust optimization

Electricity storage is used for intertemporal price arbitrage and for ancillary services that balance unforeseen supply and demand fluctuations via frequency regulation. We present an optimization model that computes bids for both arbitrage and frequency regulation and ensures that storage operators can honor their market commitments at all times for all fluctuation signals in an … Read more

Out-of-the-Box Global Optimization for Packing Problems: New Models and Improved Solutions

Published: 2026/05/04

Global Optimization, Nonlinear Optimization

Recent LLM-driven discoveries have renewed interest in geometric packing problems. In this paper, we study several classes of such packing problems through the lens of modern global nonlinear optimization. Starting from comparatively direct nonlinear formulations, we consider packing circles in squares and fixed-perimeter rectangles, packing circles into minimum-area ellipses, packing regular polygons into regular polygons, … Read more

Decomposition-Based Reformulation of Nonseparable Quadratic Expressions in Convex MINLP

Published: 2026/04/11

(Mixed) Integer Nonlinear Programming, Convex Optimization, Global Optimization Convex Mixed-Integer Programming, Eigendecomposition, LDLT Decomposition, Lifting Reformulations, Mixed-integer nonlinear programming (MINLP), Quadratic Decomposition, supporting hyperplane optimization toolkit (shot)

In this paper, we present a reformulation technique for convex mixed-integer nonlinear programming (MINLP) problems with nonseparable quadratic terms. For each convex non-diagonal matrix that defines quadratic expressions in the problem, we show that an eigenvalue or LDLT decomposition can be performed to transform the quadratic expressions into convex additively separable constraints. The reformulated problem … Read more

Separable QCQPs and Their Exact SDP Relaxations

Published: 2026/04/03

Global Optimization Theory, Quadratic Programming, Semi-definite Programming exact relaxation, horizontal connection, new rank-based exactness results, semidefinite programming relaxation, Separable QCQP, structured bilevel optimization.

This paper studies exact semidefinite programming relaxations (SDPRs) for separable quadratically constrained quadratic programs (QCQPs). We consider the construction of a larger separable QCQP from multiple QCQPs with exact SDPRs. We show that exactness is preserved when such QCQPs are combined through a separable horizontal connection, where the coupling is induced through the right-hand-side parameters … Read more

Hardness of some optimization problems over correlation polyhedra

Published: 2026/03/20

(Mixed) Integer Nonlinear Programming, Global Optimization Theory, Polyhedra boolean quadric polytope, cone, cut polytope, matrix decomposition

We prove the NP-hardness, using Karp reductions, of some problems related to the correlation polytope and its corresponding cone, spanned by all of the n×n rank-one matrices over {0, 1}. The problems are: membership, rank of the decomposition, and a “relaxed rank” obtained from relaxing the zero-norm expression for the rank to an ℓ1 norm. … Read more