Pershing Square Renew, a public-private partnership focused on renovating the park, announced the finalists this week. The competition was launched in September and drew 54 team entries.
"The world-class firms selected by our jury represent a huge range," said Eduardo Santana, executive director of Pershing Square Renew. "They include global stars and local unknowns."
Totalling five acres (two hectares), the 150-year-old park covers an entire city block in downtown LA. It sits adjacent to a jewellery district and civic centre, as well as a major transit station.
The park has been criticised for the walls surrounding it and raised entryways, which deter people from using the space.
LA studios Morphosis, the firm behind controversial plans for a 381-metre-tall mirrored hotel tower in Vals, Switzerland, and SWA teamed up to create a schemed called Local Force.
"We have developed an approach that focuses on four big ideas that ask the question: what if?" said the firms. "Each idea is developed into a scene inspired by the notion that Pershing Square will be an urban stage in which the public life of downtown Los Angeles will be playing out every day."
One idea is Ecotopia, which calls for a park with botanical gardens, water pools and a green lawn, a stormwater collection system and a demonstration facility for sewer-mining. Others involve improving public transportation amenities in the park and creating "rooms" that are programmed for day and evening usage.
A scheme called Landscape Starchitects was proposed by New York-based James Corner Field Operations – one of the firms behind the hugely successful High Line park in Manhattan – and LA studio Frederick Fisher & Partners.
The scheme proposes a variety of specific actions, including the creation of a downtown art and culture walk, the instalment of iconic gateways, and minimising barriers such as ramps and planter walls.
It also involves the addition of thematic gardens, among other elements
Their conceptual scheme explores themes such as social and natural ecologies, food culture and food security, and syncing urban hardware and software.
Pershing Square has been through various upgrades, the most recent being an overhaul in the early 1990s designed by the late Mexican architect Ricardo Legorreta and LA-based landscape architect Laurie Olin.
The Postmodern-style renovations included a 10-storey purple bell tower, a concert stage, fountains and small plazas.
LA Times architecture critic Christopher Hawthorne has described the park as a "perfectly depressing symbol of LA's neglected public realm".
"The square was once the most vibrant public space in Los Angeles," he wrote in 2013. "The decision to build a parking garage beneath it in the 1950s added entry and exit ramps that cut the square off from the sidewalks around it. A 1993 redesign somehow made that sense of disconnection worse."
But LA has recently started to enjoy an architectural renaissance. In September, leading studios told Dezeen that LA has become "the hottest destination" in America for international architects, with a number of high profile projects and competitions.
LA councillor Jose Huizar initiated the establishment of Pershing Square Renew, the public-private partnership dedicated to revitalising the park, this year.
The organisation launched its international design competition for the park in September and announced 10 semifinalists in late October.
The four finalists will develop their proposals in the first quarter of 2016, leading to another round of jury interviews and a public presentation in March. The public will be invited to comment on each of the proposals.
"Pershing Square is one step closer to once again becoming the focal point of life, commerce and civic engagement in downtown Los Angeles," said Huizar. "This design competition has allowed hundreds of the most creative architectural and design experts in the world to focus their attention on the city's oldest park."
See the proposals from the four design teams:
Globetrotters by Agence TER and SALT Landscape Architects
Wild Card by wHY and Civitas
Local Force by SWA and Morphosis
Landscape Starchitect by James Corner Field Operations and Frederick Fisher & Partners
Sign up for a daily roundup
of all our stories