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In this paper we propose a linear scalarization proximal point algorithm for solving arbitrary lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and using the condition that the proximal…
In this note, we show that the L2 optimal solutions to most real multiple view L2 triangulation problems can be efficiently obtained by two-stage Newton-like iterative methods, while the difficulty of such problems mainly lies in how to…
The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…
We provide a unified analysis of two-timescale gradient descent ascent (TTGDA) for solving structured nonconvex minimax optimization problems in the form of $\min_\textbf{x} \max_{\textbf{y} \in Y} f(\textbf{x}, \textbf{y})$, where the…
Numerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and…
A key challenge in decentralized optimization is determining the optimal convergence rate and designing algorithms to achieve it. While this problem has been extensively addressed for doubly-stochastic and column-stochastic mixing matrices,…
We address day-ahead transmission topology planning and congestion management as a sequential, multi-objective optimization problem and develop two complementary algorithms for it: an exact enumeration method and a tailored evolutionary…
This paper presents a computationally efficient model predictive control formulation that uses an integral Chebyshev collocation method to enable rapid operations of autonomous agents. By posing the finite-horizon optimal control problem…
In this paper we propose a general framework to characterize and solve the stochastic optimization problems with multiple objectives underlying many real world learning applications. We first propose a projection based algorithm which…
Multivariate adaptive regression splines (MARS) is a flexible statistical modeling method that has been popular for data mining applications. MARS has also been employed to approxmiate unknown relationships in optimzation for complex…
In multiobjective optimisation, a set of scalable test problems with a variety of features allow researchers to investigate and evaluate the abilities of different optimisation algorithms, and thus can help them to design and develop more…
Multi-scale deformable attention (MSDA) is a flexible and powerful feature extraction mechanism for visual tasks, but its random-access grid sampling strategy poses significant optimization challenges, especially on domain-specific…
Distributed stochastic optimization, arising in the crossing and integration of traditional stochastic optimization, distributed computing and storage, and network science, has advantages of high efficiency and a low per-iteration…
For the purpose of addressing the multi-objective optimal reactive power dispatch (MORPD) problem, a two-step approach is proposed in this paper. First of all, to ensure the economy and security of the power system, the MORPD model aiming…
The multi-objective optimization is to optimize several objective functions over a common feasible set. Since the objectives usually do not share a common optimizer, people often consider (weakly) Pareto points. This paper studies…
A common goal in evolutionary multi-objective optimization is to find suitable finite-size approximations of the Pareto front of a given multi-objective optimization problem. While many multi-objective evolutionary algorithms have proven to…
We propose two variants of the Primal Dual Hybrid Gradient (PDHG) algorithm for saddle point problems with block decomposable duals, hereafter called Multi-Timescale PDHG (MT-PDHG) and its accelerated variant (AMT-PDHG). Through novel…
Multi-Objective Optimization (MOO) is an important problem in real-world applications. However, for a non-trivial problem, no single solution exists that can optimize all the objectives simultaneously. In a typical MOO problem, the goal is…
In this paper, we deal with the Front Steepest Descent algorithm for multi-objective optimization. We point out that the algorithm from the literature is often incapable, by design, of spanning large portions of the Pareto front. We thus…
This paper presents a new implementation of deterministic multiobjective (MO) optimization called Multiobjective Fractal Decomposition Algorithm (Mo-FDA). The original algorithm was designed for mono-objective large scale continuous…