Search · four archives
Search · four archives
16 papers · ranked by Valyu relevance
Cody Karcher, Robert Haimes
A method of Sequential Log-Convex Programming (SLCP) is constructed that exploits the log-convex structure present in many engineering design problems. The mathematical structure of Geometric Programming (GP) is combined with the ability of Sequential Quadratic Program (SQP) to accommodate a wide range of objective and…
Dongchan Lee, Konstantin Turitsyn, Jean-Jacques Slotine
This paper presents a convex sufficient condition for solving a system of nonlinear equations under parametric changes and proposes a sequential convex optimization method for solving robust optimization problems with nonlinear equality constraints. By bounding the nonlinearity with concave envelopes and using…
Jérôme Bolte, Edouard Pauwels
In view of solving nonsmooth and nonconvex problems involving complex constraints (like standard NLP problems), we study general maximization-minimization procedures produced by families of strongly convex sub-problems. Using techniques from semi-algebraic geometry and variational analysis –in particular Lojasiewicz…
Milad Dehghani Filabadi, Chen Chen
Signomial geometric programming (SGP) is a computationally challenging, NP-Hard class of nonconvex nonlinear optimization problems. SGP can be solved iteratively using a sequence of convex relaxations; consequently, the strength of such relaxations is an important factor to this iterative approach. Motivated by recent…
Yuanqi Mao, Daniel Dueri, Michael Szmuk, Behçet Açıkmeşe
This paper presents a Successive Convexification (SCvx) algorithm to solve a class of non-convex optimal control problems with certain types of state constraints. Sources of nonconvexity may include nonlinear dynamics and non-convex state/control constraints. To tackle the challenge posed by non-convexity, first we…
Jingwen Ren, Mark JP Chaisson
It is computationally challenging to detect variation by aligning long reads from single-molecule sequencing (SMS) instruments, or megabase-scale contigs from SMS assemblies. One approach to efficiently align long sequences is sparse dynamic programming (SDP), where exact matches are found between the sequence and the…
Yoshinari Takayama, Kazumune Hashimoto, Toshiyuki Ohtsuka
—Signal Temporal Logic (STL) is capable of expressing a broad range of temporal properties that controlled dynamical systems must satisfy. In the literature, both mixedinteger programming (MIP) and nonlinear programming (NLP) methods have been applied to solve optimal control problems with STL specifications. However…
Sandy Bitterlich, Radu Ioan Boţ, Ernö Robert Csetnek, Gert Wanka
The Alternating Minimization Algorithm has been proposed by Paul Tseng to solve convex programming problems with two-block separable linear constraints and objectives, whereby (at least) one of the components of the latter is assumed to be strongly convex. The fact that one of the subproblems to be solved within the…
Lirong Wang, Zhijun Luo
A simple sequential quadratic programming method is proposed to solve the constrained minimax problem. At each iteration, through introducing an auxiliary variable, the descent direction is given by solving only one quadratic programming. By solving a corresponding quadratic programming, a high-order revised direction…
Radu Ioan Boţ, Ernö Robert Csetnek, Dang-Khoa Nguyen
This work aims to minimize a continuously differentiable convex function with Lipschitz continuous gradient under linear equality constraints. The proposed inertial algorithm results from the discretization of the second-order primal-dual dynamical system with asymptotically vanishing damping term addressed by Boţ and…
Radu Ioan Boţ, Ernö Robert Csetnek
In this paper, we propose two proximal-gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a smooth function, either concave or convex. In the iterative schemes, we perform a proximal step with…
David P. Morton, Oscar Dowson, Bernardo K. Pagnoncelli
We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous action and state spaces. We extend policy graphs to include decision-dependent uncertainty for one-step transition probabilities as well as…
Oliver Serang, Jérémie Bourdon
Linear programming (LP) problems are commonly used in analysis and resource allocation, frequently surfacing as approximations to more difficult problems. Existing approaches to LP have been dominated by a small group of methods, and randomized algorithms have not enjoyed popularity in practice. This paper introduces a…
Authors not listed
Solving optimization problems, especially for nonlinear and constrained systems, is a challenge. Decades of specialized algorithms have been developed for general and special cases of root finding, minimization (including constraints), for parameter estimation, and mapping connected spaces. These approaches typically…
V. M. Veliov, P. T. Vuong
The paper presents new results about convergence of the gradient projection and the conditional gradient methods for abstract minimization problems on strongly convex sets. In particular, linear convergence is proved, although the objective functional does not need to be convex. Such problems arise, in particular, when…
Peter L. Bartlett, Chris Junchi Li, Jingfeng Wu, Bin Yu
In the field of optimization, developing accelerated methods for solving minimax and fixed-point problems remains a fundamental challenge. This paper presents a novel family of dual accelerated algorithms that achieve optimal convergence rates for both minimax and fixed-point problems. By exploring new anchoring…